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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`
`(sqrt5 + 1)/sqrt2`
Solution
We know that rationalization factor of the denominator is `sqrt2`.We will multiply numerator and denominator of the given expression `(sqrt5 + 1)/sqrt2` by `sqrt2` to get
`(sqrt5 + 1)/sqrt2 xx sqrt2/sqrt2 = (sqrt10 + sqrt2)/(sqrt2 xx sqrt2)`
`= (sqrt10 + sqrt2)/2`
`= (3.162 + 1.414)/2`
= 4.576/2
= 2.288
The value of expression 2.288 can be round off to three decimal places as 2.288.
Hence the given expression is simplified to 2.288.
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