Question

which of the following is equivalent to the quotient below? √16/3√2

Answer 1

Explanation:

The expression that we have is:

$\frac{\sqrt{16}}{3\sqrt{2}}$

And we need to find the equivalent expression.

Step 1. First, we solve the square root of 16 which is 4:

$\frac{4}{3\sqrt{2}}$

Step 2. Then, to eliminate the square root in the denominator, we multiply the expression by:

$\frac{4}{3\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}$

This is a multiplication by 1 and it does not affect the expression but it will help us to eliminate the square root in the denominator.

Step 3. Simplifying:

$\begin{gathered} \frac{4\sqrt{2}}{3(\sqrt{2})^2} \\ \downarrow \\ \frac{4\sqrt{2}}{3\cdot2} \\ \downarrow \\ \frac{4\sqrt{2}}{6} \end{gathered}$

Step 4. The final step is to simplify the 4/6 by 2/3, which is an equivalent fraction, and this is the final result:

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

which is shown in option B.

Answer: Option B.