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Math Help - Straight Forward way to get the square root of a fraction.

  1. #1
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    Straight Forward way to get the square root of a fraction.

    Hi All,
    Without using a calculator is their a straighforward way of computing the following to come to the correct answer (not educated guess based on closed square).

    1. SQRT(68/5)

    or indeed a decimal: SQRT(62.5)

    Thanks in Advance.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by dumluck View Post
    Hi All,
    Without using a calculator is their a straighforward way of computing the following to come to the correct answer (not educated guess based on closed square).

    1. SQRT(68/5)

    or indeed a decimal: SQRT(62.5)

    Thanks in Advance.
    One way is

    \displaystyle\frac{\sqrt{68}}{\sqrt{5}}=\frac{\sqr  t{64+4}}{\sqrt{4+1}}=\frac{2\sqrt{16+1}}{2\sqrt{1+  \frac{1}{4}}}=\frac{4\sqrt{1+\frac{1}{16}}}{\sqrt{  1+\frac{1}{4}}}=4\frac{\sqrt{1+\frac{1}{2^4}}}{\sq  rt{1+\frac{1}{2^2}}}

    \displaystyle\sqrt{62.5}=\sqrt{\frac{625}{10}}=\fr  ac{\sqrt{625}}{\sqrt{10}}=\frac{25}{\sqrt{9+1}}=\f  rac{25}{3\sqrt{1+\frac{1}{9}}}=\frac{25}{3\sqrt{1+  \frac{1}{3^2}}}

    You could try expanding a few terms of the power series.
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