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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`

`2/sqrt3`

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#### Solution

We know that rationalization factor of the denominator is `sqrt3`. We will multiply numerator and denominator of the given expression `2/sqrt3` by `sqrt3` to get

`2/sqrt3 xx sqrt3/sqrt3 = (2 xx sqrt3)/(sqrt3 xx sqrt3)`

`= (2sqrt3)/3`

`= (2 xx 1.732)/3`

`= 3.4641/3`

= 1.1547

The value of expression 1.1547 can be round off to three decimal places as 1.155

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#### RELATED QUESTIONS

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`(sqrt5 - 2)(sqrt3 - sqrt5)`

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`(sqrt5 - sqrt3)^2`

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`(6 - 4sqrt2)/(6 + 4sqrt2)`

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`(2 + sqrt(3))/(2 - sqrt(3))`

Rationalise the denominator in each of the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.

`sqrt(2)/(2 + sqrt(2)`