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Rationalise the denominator of the following:

`3/(2sqrt5)`

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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/(2sqrt5)` by `sqrt5`to get

`3/(2sqrt5) xx sqrt5/sqrt5 = (3sqrt5)/(2sqrt5 xx sqrt5)`

`= (3sqrt5)/(2xx5)`

`= (3sqrt5)/10`

Hence the given expression is simplified to `(3sqrt5)/10`

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#### RELATED QUESTIONS

Express the following with rational denominator:

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

Rationales the denominator and simplify:

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

Write the reciprocal of \[5 + \sqrt{2}\].

If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\] find the values of *x *and *y*.

If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].

Rationalise the denominator of the following:

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

Rationalise the denominator of the following:

`(3sqrt(5) + sqrt(3))/(sqrt(5) - 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.

`6/sqrt(6)`

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.

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

Simplify:

`[((625)^(-1/2))^((-1)/4)]^2`