Problem 53930. Easy Sequences 65: Fractional Part of Square Roots

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The </w:t></w:r><w:hyperlink w:docLocation=\"https://brilliant.org/wiki/factional-part-function/\"><w:r><w:t>fractional part function</w:t></w:r></w:hyperlink><w:r><w:t> of a positive real number </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r</w:t></w:r></w:customXml><w:r><w:t>, denoted as </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{r\\}</w:t></w:r></w:customXml><w:r><w:t>, is defined as: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{r\\}=r-\\lfloor r \\rfloor</w:t></w:r></w:customXml><w:r><w:t>, where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\lfloor r \\rfloor</w:t></w:r></w:customXml><w:r><w:t>, is the 'floor' of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r</w:t></w:r></w:customXml><w:r><w:t>. Thus, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{ \\sqrt 2 \\}=0.41421...</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{ \\pi \\}=0.14159...</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{10\\}=0</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given a positive integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, create the function </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>FPSR(n)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, that evaluates the following summation:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>FPSR(n) = \\sum_{r=1}^n \\{ \\sqrt r \\}</w:t></w:r></w:customXml><w:r><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=10</w:t></w:r></w:customXml><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>FPSR(10) = \\sum_{r=1}^{10} \\{ \\sqrt r \\} = \\{ \\sqrt 1 \\}+\\{ \\sqrt 2 \\}+\\{ \\sqrt 3 \\}+\\{ \\sqrt 4 \\}+\\{ \\sqrt 5 \\}+\\{ \\sqrt 6 \\}+\\{ \\sqrt 7 \\}+\\{ \\sqrt 8 \\}+\\{ \\sqrt 9 \\}+\\{ \\sqrt {10} \\}\\\\\n\\ \\ \\ \\ \\ \\ \\ \\&gt;\\&gt;\\&gt; = 0+0.41421...+0.73205...+0+0.23606...+0.44948...+0.64575...+0.82842...+0+0.16227...\\\\\n\\ \\ \\ \\ \\ \\ \\ \\&gt;\\&gt;\\&gt; = 3.46827...</w:t></w:r></w:customXml><w:r><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Please present the function output rounded-off to nearest integer. Therefore, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=10</w:t></w:r></w:customXml><w:r><w:t>, the function should return </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>3</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>HINT:</w:t></w:r><w:r><w:t> There are efficient algorithms to </w:t></w:r><w:hyperlink w:docLocation=\"https://math.stackexchange.com/questions/1277652/calculate-fractional-part-of-square-root-without-taking-square-root\"><w:r><w:t>calculate fractional part of square root</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 400px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">The <a target='_blank' href = "https://brilliant.org/wiki/factional-part-function/">fractional part function</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> of a positive real number r<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, denoted as <img src="data:image/png;base64,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" width="24.5" height="19" style="width: 24.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, is defined as: <img src="data:image/png;base64,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" width="86.5" height="19" style="width: 86.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, where <img src="data:image/png;base64,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" width="23" height="19" style="width: 23px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, is the 'floor' of r<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. Thus, <img src="data:image/png;base64,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" width="121.5" height="21" style="width: 121.5px; height: 21px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, <img src="data:image/png;base64,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" width="105.5" height="19" style="width: 105.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> and <img src="data:image/png;base64,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" width="59" height="19" style="width: 59px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.</div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">Given a positive integer n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, create the function <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAAmCAYAAAAYws+cAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAcqADAAQAAAABAAAAJgAAAAC97fsdAAAIPElEQVR4Ae2YebCXUxjHb5QlLRQm1UiRkqzZhVuyRobBUKHIEMbWWGsyKBQGQxMqy4w1MvxhQtFCjCVSQspOiAxFRJbPtzlP9+n0Lr97+907U73fme89z3me533O+z7nnOec362oKFBkoMhAkYEiA0UGigwUGViPM7DxevxtdflplQzWEP5YpkFPIs7P8PcyxVunw9Sro7cfyDjPwnJuinbEext2hCUh72OPIcpxcKOSoq3udA/duUF1Mm13mDTev+i1khfCBXAqlC4LTTBeAXvADlD+8+EL8HV4KNwBngENRyP0gknvIJ8l8Cv4KZwMV8A8HIHDcNgNlnv37E/M++AhcClca2xOhDHwP8cJyIPg+fAieBUcDd+F5tcG2aMlnVnQ7H8gK0YfOBhqImT7HJ4D07ArhkXwb3gDbA8bw33hWGjxL0WO0RzFNGg+/yBrInrDa+E8KNvX8FyYhe0wzoFqawunEvipcgY/nWD28bORs3bo7diV6CSMRGlxJHvUpzMJmt3vJvPTovow+Aw1ZdQ+GexdI711hwS7xtHEe2xC5xVo73C2NzpZ3y+/y52utsTpBL6sXMFvJJB93LCcoAdgfz7FZ6KLo/IXYy8UNo5KXIwjUZi9U2wMfflopzVKsY9HbzF0qYhxIAqzfxEbQ1+L4Vu4WYq9nGqVbVWf3coR1K/StJVu4+yBcJ11XKsdp3NISfoVqh9jUxSaBEtks8hB5c9srSObdVXCtWvToAlQDCWnaYKTdDaGWpVjjwZ0dKbrWKgr6NzXnWOtoJW9HOqjfoFJE4B6NSRdKLQDLUHPrOZd1dkS8d/g9yetJtZDybMYZ3mDk/XMGNf3Ymc69vxr3uDk3Z2PJiz+luODXZesuoIqwGIY52PV+FlnnTlVIujsECbDFSul1f/ElxMlK8ZRTqHbZRJU1ixxbyFrAXlIZxiJ0Mo6rtUzaRcV/w4vume8eLjrvIwcf8uZ6LSr5zm/PFGLf8cEp53Q6dzPwxQcVJ10664x7uZJW8UDEqJop41L0MeqmSgszvaxMfQfdj59E3xU1uY4n9nIcflNeGyVSpNn77DfKm2VoN2onxHy+Qq2gB4N6ahS6D2zoJ1zAVRleBvqhu6rkM5xxdc4S6F2eRb03b9BXeRqjE940j6+tYuikqsVovLT0+mTxG1RWslMO79uw8fGuT8pSNAp2Uuc7zvITYItq9HKV0I1xk/QqpHatnAEVLJknws1Tgz9QJf96tgQ9bUD94d3QPumfsiCfhZpQamKaWfLPgHm4X0ctChqhHY8ZS+iS8hHcD5cCO1SoouLlV7ERGh3WZxpyMcE9qEdAm2XfYd8GcyLpxL5F7SYU5HzbpB6xvy1qLQjFsDlQa/JfRz2hhvDJPRAqRhJlSnJ/4Dgr1xtDU+Bd8J6UJgIFW+sOjmYgl35qREG8pR9vAbrArvC46BW1i/wUZiHR3CwOJOR34Ra9WrHw1thf5g3GbiswmlItpgUO29V346PvYO+S6X1PqdTKcxDPxwU48Q8x2C/Jvi/SrsnVK5sEhErPoOKd5E6OXgauxagymy18SxP2MdrRcd4DMVJsTLq68UXQcXR6m8Iy4XzCWTvp1YTlIYPMMhHk79VcGpLayW/lLI1BH/FOCQ8n9dMCf6DaZ+D/gjQcaNYYgeYB1t0bfIcY7tm3s4inS2bxw70n4B5E6NdbC/8ckKMtVWNcvEXIyft6lbOR1XAYwode7/O3pAgXxl8uyXYYlUjFFq4ij0eHgw9Tqcj25demSGPC/4tk3zswE+yHYiycTBMp9VkxngQxbJYGfWPdv2XnFwdsX2G8yBss4O9GW1Sko90z09yskR9g6G/CSntN0HfPMXu1ZV0dNarAnwPZ0APe6cXvTJD1hm7AirWGsiaSD8BaYOl6f1APk5NJlIl6AofMJL1c2Cs07V2son+WIgnUmfP0uDYl7a+PZTQVmcibaL+Is6whFhHBF2pOdHi0WVHR0G1MBNvbX1x12o9WeWsf3f9DRXjB1gPVhc6j+LkxzG6orB3tQSZjxbrT8GuCWtgBteOCXbFOMHpY7Fd8BscGxL6Hwdfv8jMrVOwraC189psaa3ivZFmTNNrF9gl4Ns0pxL0ughZgh8vwT/JZQDKRVBlKg2nYrBx4rK3r7M9nxLgIOejC14a9A5aDBPSHIK+Da29T/cE30uC3SZGi01HWRp0SdKkj05zUIAknIzSdo+uzjXF8e7BGU6ujrgzztvAizMe0kQKT8DFK6WqP72qxDXOKTO9jjAvdHrStjZD1KpMPgUrYVruMFVYVfgReaoUEewct8ufSu9mkY/vVtLRb9tHvTJP1gP6KFtR9+c9kGJvgf5XF0c7qybQtV3vsgyeFQVQMq+Gsn8Dddnx0O78Htq3jPDGSLY48n0osvmuSr189vbKSNZkZ8X5KNhvob0ZDoJZuAvjp9A2V5bvStuF/J0F7cPVakurlJwHS8U9OH4HfZwl9B+Gu8DqQL//VFLGQZXY9+C98AH4MdQYj0EdBx5a5QuhfwfdvLWq94ExWqLQt5q/Yh8bO4X+AtqbUmzaCD9DxdHRkoRRKGXXDtcCykJ9jJ/D67Oc1gVbT/eS2oEHQZ0xQ6FKantY1ziXAbUw4/O41PfQzuoCW5TwgMbSpogXagmPFi6lZEBVQKWxNrEJwbUbu9fmIBt67C1IwDtQt+LawnACX1dbwYu4VRnoiDgftqlSlU3qTyTdarNux2UbrAhUUXEYSdBPtKZlTMbhxNI/QUr9Z0EZh96wQ7Xi87cvYwp0q25QxnhFqCIDRQaKDBQZKDJQZKDIwLqdgf8BMksFyBCu4UIAAAAASUVORK5CYII=" width="57" height="19" style="width: 57px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, that evaluates the following summation:</div><div style="block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> <img src="data:image/png;base64,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" width="139" height="46" style="width: 139px; height: 46px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> </div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">For example for <img 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" width="725" height="89" style="width: 725px; height: 89px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> </div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">Please present the function output rounded-off to nearest integer. Therefore, for <img src="data:image/png;base64,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" width="44" height="18" style="width: 44px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, the function should return 3<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">HINT:<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> There are efficient algorithms to <a target='_blank' href = "https://math.stackexchange.com/questions/1277652/calculate-fractional-part-of-square-root-without-taking-square-root">calculate fractional part of square root</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">.</div></div></div>

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Problem 53930. Easy Sequences 65: Fractional Part of Square Roots

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Problem 53930. Easy Sequences 65: Fractional Part of Square Roots

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