Question

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Which expression is equivalent to √60x^3
?

(1 point)
Responses

4x215x−−−√
4 x squared square root of 15 x

2x230x−−−√
2 x squared square root of 30 x

2x15x−−−√
2 x square root of 15 x

30x3
30 x cubed
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Answer 1

To simplify the expression \( \sqrt{60x^3} \), we can break it down as follows:

1. Factor \( 60 \) into its prime factors: \( 60 = 4 \times 15 = 2^2 \times 15 \).
2. Rewrite \( x^3 \) as \( x^2 \times x \).
3. We can now express \( \sqrt{60x^3} \) as:
\[
\sqrt{60x^3} = \sqrt{4 \times 15 \times x^2 \times x} = \sqrt{4} \times \sqrt{15} \times \sqrt{x^2} \times \sqrt{x}
\]
4. Calculating the square roots:
\[
\sqrt{4} = 2, \quad \sqrt{x^2} = x
\]
Thus, we get:
\[
\sqrt{60x^3} = 2x\sqrt{15x}
\]

Now comparing the options provided:

1. \( \mathbf{4x^2\sqrt{15x}} \)
2. \( \mathbf{2x^2\sqrt{30x}} \)
3. \( \mathbf{2x\sqrt{15x}} \)
4. \( \mathbf{30x^3} \)

The correct equivalent expression is \( 2x\sqrt{15x} \).

So the answer is:
**2x15x−−−√** (2 x square root of 15 x)