Respuesta :

carlosego

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

[tex]\sqrt {12} * \sqrt {18}[/tex]

We combine using the product rule for radicals:

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

So, we have:

[tex]\sqrt {12 * 18} =\\\sqrt {216} =[/tex]

We rewrite the 216 as[tex]6 * 6 * 6 = 6 ^ 3 = 6 ^ 2 * 6[/tex]

[tex]\sqrt {6 ^ 2 * 6} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a[/tex]

Then, the expression is:

[tex]6 \sqrt {6}[/tex]

Answer:

Option D

kudzordzifrancis

ANSWER

[tex]6 \sqrt{6} [/tex]

EXPLANATION

The given product is

[tex] \sqrt{12} \times \sqrt{18} [/tex]

We rewrite to get;

[tex] \sqrt{4 \times 3} \times \sqrt{9 \times 2} [/tex]

We split the radical sign to get:

[tex]\sqrt{4 } \times \sqrt{3} \times \sqrt{9} \times \sqrt{2} [/tex]

The perfect squares simplifies to:

[tex]2\sqrt{3} \times 3 \sqrt{ 2} [/tex]

This gives us :

[tex]2 \times 3 \sqrt{3 \times 2} [/tex]

This simplifies to;

[tex]6 \sqrt{6} [/tex]

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