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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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Solution
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
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