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Question

Which expression is equivalent to 60x^3−−−−√
?

Answer 1

To simplify the expression \( \sqrt{60x^3} \), we can break it down into its components.

1. First, factor \( 60 \): \[ 60 = 4 \times 15 = 4 \times 3 \times 5 \]

2. Using the property of square roots that \( \sqrt{ab} = \sqrt{a} \cdot \sqrt{b} \), we can express \( \sqrt{60x^3} \) as: \[ \sqrt{60x^3} = \sqrt{60} \cdot \sqrt{x^3} \]

3. Now simplify \( \sqrt{x^3} \): \[ \sqrt{x^3} = \sqrt{x^2 \cdot x} = \sqrt{x^2} \cdot \sqrt{x} = x\sqrt{x} \]

4. Next simplify \( \sqrt{60} \): \[ \sqrt{60} = \sqrt{4 \cdot 15} = \sqrt{4} \cdot \sqrt{15} = 2\sqrt{15} \]

5. Combine everything: \[ \sqrt{60x^3} = \sqrt{60} \cdot \sqrt{x^3} = 2\sqrt{15} \cdot x\sqrt{x} = 2x\sqrt{15x} \]

Thus, the expression equivalent to \( \sqrt{60x^3} \) is: \[ 2x\sqrt{15x} \]