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

Which of the following is equivalent to the quotient below? √16/3√2-example-1
User Atul Kumar
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1 Answer

3 votes

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.

User Cartina
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