Sandra was simplifying 4√5×2√3, and she ended up with 8√15 as her simplified answer. Is Sandra correct? If she is not correct, what was her mistake?

Answer 1

To simplify \( 4\sqrt{5} \times 2\sqrt{3} \), we follow the order of operations by multiplying the coefficients and the square roots separately.

1. Multiply the coefficients: \[ 4 \times 2 = 8 \]

2. Multiply the square roots: \[ \sqrt{5} \times \sqrt{3} = \sqrt{5 \times 3} = \sqrt{15} \]

3. Combine the results: \[ 4\sqrt{5} \times 2\sqrt{3} = 8 \times \sqrt{15} = 8\sqrt{15} \]

Sandra's answer of \( 8\sqrt{15} \) is indeed correct. Therefore, she did not make a mistake in her simplification.