Question

Simplify 4sqrt(6) / sqrt(30) by rationalizing the denominator.

Answer 1

Given question is 4√6/√30
by rationalizing the denominator
4√6x√30/√30x√30
= 4√6x30/√30²
=4x√180/30 (i)
by solving the √180
√180=6√5
putting the value of √180 in (i)
=4x6√5/30
=24√5/30
=4√5/5 is the right answer.

Answer 2

The simplified expression of $\frac{4\sqrt{6}}{\sqrt{30}}$ is $\frac{4\sqrt{5}}{5}$

How to simplify the expression?

The expression is given as:

$\frac{4\sqrt{6}}{\sqrt{30}}$

Rationalize the expression

$\frac{4\sqrt{6 * 30}}{\sqrt{30 * 30}}$

Evaluate the products

$\frac{4\sqrt{6 * 30}}{30}$

Evaluate the exponent of the product of 6 and 30

$\frac{4 * 6\sqrt{5}}{30}$

This gives

$\frac{24\sqrt{5}}{30}$

Divide 24 and 30 by 6

$\frac{4\sqrt{5}}{5}$

Hence, the simplified expression of $\frac{4\sqrt{6}}{\sqrt{30}}$ is $\frac{4\sqrt{5}}{5}$

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