Question

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt10 + sqrt15)/sqrt2`

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Answer 1

We know that rationalization factor of the denominator is `sqrt2`. We will multiply numerator and denominator of the given expression `(sqrt10 + sqrt15)/sqrt2` by `sqrt2` to get

`(sqrt10 + sqrt15)/sqrt2 xx sqrt2/sqrt2 = (sqrt10 xx sqrt2 + sqrt15 xx sqrt2)/(sqrt2 xx sqrt2)`

`= (sqrt10 xx sqrt2 + sqrt5 xx sqrt3 xx sqrt2)/2`

`= (3.162 xx 1.414 + 2.236 xx 1.732 xx 1.414)/2`

`= 9.947/2`

= 4.9746

The value of expression 4.9746 can  be round off to three decimal places as 4.975.

Hence the given expression is simplified to 4.975