Question

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

Answer 1

Explanation:

The expression that we have is:

`(√(16))/(3√(2))`

And we need to find the equivalent expression.

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

`(4)/(3√(2))`

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

`(4)/(3√(2))\cdot(√(2))/(√(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} (4√(2))/(3(√(2))^2) \\ \downarrow \\ (4√(2))/(3\cdot2) \\ \downarrow \\ (4√(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:

`(2√(2))/(3)`

which is shown in option B.

Answer: Option B.