Question

Using the ratio of perfect squares method, what is square root of 59 rounded to the nearest hundredth?

Answer 1

$\frac{59}{100} =0.59 \\ \sqrt{ \frac{59}{100} } = \sqrt{0.59} \\ \frac{ \sqrt{59} }{10} = \sqrt{0.59} \\ \sqrt{59} =10 \times \sqrt{0.59}$
Now
$0.59= \frac{100}{169} \\ \sqrt{0.59} = \sqrt{ \frac{100}{169} } = \frac{10}{13} =0.769$
Therefore,
$\sqrt{59} =10 \times 0.769=7.69$