Question

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Answer 1

Option B

$3 x\sqrt{2} x$ is the choice equivalent to $\sqrt{6} x^{2} \cdot \sqrt{3} x$

Solution:

Step 1:

When we multiply two roots i.e. $\sqrt{6} x^{2}$ and $\sqrt{3} x$ the values are multiplied and still kept inside the root.

So $\sqrt{6} x^{2}$ × $\sqrt{3} x$ = $\sqrt{6} x^{2} \times 3 x$.

Step 2:

We then multiply the values in the root.

$\sqrt{6} x^{2} \times 3 x$ = $\sqrt{18 x^{3}}$

Step 3;

We take the values out of the root by splitting up the value.

${18 x^{3}}$ = $(9 \times 2)\left(x^{2} \times x\right)$

$\sqrt{9}=3$ and $\sqrt{x^{2}}=x$

So $\sqrt{18 x^{3}}$ = $\sqrt{9} \times 2 \times x^{2} \times x$

When we take values out of the root, we replace it with the square-rooted value on the outside.

$\sqrt{18 x^{3}}$ = $3 x \sqrt{2 x}$.

Thus option B is correct