Question

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

Answer 1

`(59)/(100) =0.59 \\ \sqrt{ (59)/(100) } = √(0.59) \\ ( √(59) )/(10) = √(0.59) \\ √(59) =10 * √(0.59)`
Now

`0.59= (100)/(169) \\ √(0.59) = \sqrt{ (100)/(169) } = (10)/(13) =0.769`
Therefore,

`√(59) =10 * 0.769=7.69`