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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`
`(sqrt2 - 1)/sqrt5`
Solution
We know that rationalization factor of the denominator is `sqrt5`. We will multiply numerator and denominator of the given expression `(sqrt2 - 1)/sqrt5`by `sqrt5` to get
`(sqrt2 - 1)/sqrt5 xx sqrt5/sqrt5 = (sqrt2 xx sqrt5 - sqrt5)/(sqrt5 xx sqrt5)`
`= (sqrt10 - sqrt5)/5`
Putting the value of `sqrt10`and `sqrt5` we get
`(sqrt10 - sqrt5)/5 = (3.162 - 2.236)/5`
`= 0.926/5`
= 0.1852
The value of expression 0.1852 can be round off tp three decimal places as 0.185.
given expression is simplified to 0.185
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