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DanielleElmas [232]
3 years ago
11

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

Mathematics
2 answers:
VARVARA [1.3K]3 years ago
8 0

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

qwelly [4]3 years ago
5 0

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

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