Question

What is the following quotient? 3 sqrt 8 / 4 sqrt 6

Answer 1

Answer:

The correct option is D) $\frac{\sqrt{3}}{2}$

Step-by-step explanation:

We need to find out the quotient of  $\frac{3\sqrt{8}}{4\sqrt{6}}$

$=\frac{3\sqrt{8}}{4\sqrt{6}}$

Rewrite the above expression;

$=\frac{3\times2 \sqrt{2}}{4\sqrt{6}}$

$=\frac{6\sqrt{2}}{4\sqrt{6}}$

Cancel out the common term from numerator and denominator,

$=\frac{3\sqrt{2}}{2\sqrt{6}}$

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

$=\frac{3}{2\sqrt{3}}$

Multiply numerator and denominator with $\sqrt{3}$

$=\frac{3\sqrt{3}}{2\sqrt{3}\sqrt{3}}$

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

$=\frac{3\sqrt{3}}{6}$

$=\frac{\sqrt{3}}{2}$

Therefore, the correct option is D) $\frac{\sqrt{3}}{2}$

Answer 2

For this case we have the following expression:
 3sqrt (8) / 4sqrt (6)
 Rewriting we have:
 3sqrt (2 * 4) / 4sqrt (6)
 3 * 2sqrt (2) / 4sqrt (6)
 6sqrt (2) / 4sqrt (6)
 3sqrt (2) / 2sqrt (6)
 3sqrt (2) / (2sqrt (2) sqrt (3))
 3 / (2sqrt (3))
 3sqrt (3) / (3 * 2)
 sqrt (3) / (2)
 Answer:
 the following quotient is:
 D.sqrt 3/2