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

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• January 7th 2011, 02:18 AM
dumluck
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.
• January 7th 2011, 04:01 AM
Archie Meade
Quote:

Originally Posted by dumluck
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.