Question

The product of 1/6 root 18 and 1/3 root18 is???

Answer 1

1/6√18*1/3√18

=1/(6*3*√18*√18)

=1/(18*18)

=1/324

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Answer 2

The product of  $\frac{1}{6\sqrt{18}} and \frac{1}{3\sqrt{18}}$  is $\frac{1}{324}$.

Given :

$\frac{1}{6\sqrt{18}} and \frac{1}{3\sqrt{18}}$

To find :

The product of $\frac{1}{6\sqrt{18}} and \frac{1}{3\sqrt{18}}$.

Concept used:

Irrational numbers of the same order a multiplied according to the following law :

ⁿ√a × ⁿ√b = ⁿ√ab

Solution :

Step 1 :

Simplify $\frac{1}{6\sqrt{18}} and \frac{1}{3\sqrt{18}}$ by multiplying them:

$\frac{1}{6\sqrt{18}} \times \frac{1}{3\sqrt{18}} = \frac{1}{(6 \times3) \times (\sqrt{18\times18})}$

$\frac{1}{6\sqrt{18}} \times \frac{1}{3\sqrt{18}} = \frac{1}{(18) \times (18)}$

$\frac{1}{6\sqrt{18}} \times \frac{1}{3\sqrt{18}} = \frac{1}{324}$

Hence, the product of $\frac{1}{6\sqrt{18}} and \frac{1}{3\sqrt{18}}$ is $\frac{1}{324}$.

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