Question

What is the following product?

Answer 1

For this case we must find the product of the following expression:

$\sqrt {12} * \sqrt {18}$

We combine using the product rule for radicals:

$\sqrt [n] {a} * \sqrt [n] {b} = \sqrt [n] {ab}$

So, we have:

$\sqrt {12 * 18} =\\\sqrt {216} =$

We rewrite the 216 as$6 * 6 * 6 = 6 ^ 3 = 6 ^ 2 * 6$

$\sqrt {6 ^ 2 * 6} =$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a$

Then, the expression is:

$6 \sqrt {6}$

Answer:

Option D

Answer 2

ANSWER

$6 \sqrt{6}$

EXPLANATION

The given product is

$\sqrt{12} \times \sqrt{18}$

We rewrite to get;

$\sqrt{4 \times 3} \times \sqrt{9 \times 2}$

We split the radical sign to get:

$\sqrt{4 } \times \sqrt{3} \times \sqrt{9} \times \sqrt{2}$

The perfect squares simplifies to:

$2\sqrt{3} \times 3 \sqrt{ 2}$

This gives us :

$2 \times 3 \sqrt{3 \times 2}$

This simplifies to;

$6 \sqrt{6}$