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Rationalise the denominator of each of the following

`3/sqrt5`

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#### Solution

We know that rationalization factor for `1/sqrta` is `sqrta` We will multiply numerator and denominator of the given expression `3/sqrt5` by `sqrt5`to get

`3/sqrt5 xx sqrt5/sqrt5 = (3sqrt5)/(sqrt5 xx sqrt5)`

`= (3sqrt5)/5`

Hence the given expression is simplified to `(3sqrt5)/5`

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#### RELATED QUESTIONS

Rationalise the denominator of the following :-

`1/sqrt7`

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`

Rationales the denominator and simplify:

`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`

In the following determine rational numbers *a* and *b*:

`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`

The rationalisation factor of \[2 + \sqrt{3}\] is

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`3sqrt(3) + 2sqrt(27) + 7/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)`

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If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.

Simplify: `(256)^(-((-3)/4^2))`