Problem

What is the following quotient?
\[
\frac{\sqrt{120}}{\sqrt{30}}
\]
2
4
$2 \sqrt{10}$
$3 \sqrt{10}$

Answer

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Answer

The quotient of the square roots is 2.0, which matches one of the answer choices. Therefore, the final answer is \(\boxed{2}\).

Steps

Step 1 :The question is asking for the quotient of two square roots. To solve this, we can use the property of square roots that says the square root of a quotient is equal to the quotient of the square roots. So, we can simplify the expression by dividing the numbers under the square roots.

Step 2 :Calculate the square root of the numerator, \(\sqrt{120}\), to get approximately 10.954451150103322.

Step 3 :Calculate the square root of the denominator, \(\sqrt{30}\), to get approximately 5.477225575051661.

Step 4 :Divide the square root of the numerator by the square root of the denominator to get the quotient, which is 2.0.

Step 5 :The quotient of the square roots is 2.0, which matches one of the answer choices. Therefore, the final answer is \(\boxed{2}\).

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