Question

Which choice is equivalent to the quotient below shown here when x>0?

Answer 1

For this case we must simplify the following expression:

$\frac {\sqrt {16x ^ 3}} {\sqrt {8x}} =$

Join the terms in a single radical:

\$\sqrt {\frac {16x ^ 3} {8x}} =\\\sqrt {\frac {8 * (2x ^ 3)} {8x}} =\\\sqrt {\frac {2x ^ 3} {8x}} =\\\sqrt {2x ^ 2} =\\\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So:

$\sqrt {2x ^ 2} =\\x \sqrt {2}$

Answer:

Option B

Answer 2

Answer:

Choice B is correct

Step-by-step explanation:

The given radical division can be expressed in the following form;

$\frac{\sqrt{16x^{3} } }{\sqrt{8x} }$

Using the properties of radical division, the expression can be expressed in the following form;

$\sqrt{\frac{16x^{3} }{8x} }=\sqrt{2x^{2} }$

Simplifying further yields;

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

Choice B is thus the correct alternative