Sandra was simplifying 4√5 . 2√3, and she ended up with 8√15

Question

as her simplified answer.

Is Sandra correct? If she is not correct, what was her mistake?

(1 point)
Responses

A. Sandra's simplified answer is correct.

B. Sandra's answer is not correct. She should have multiplied 4 times 5 in the first radical and multiplied 2 times 3 in the second radical to get a final answer of 26.

C. Sandra's answer is not correct. She should have added the coefficients to get 615−−√

D. Sandra's answer is not correct. She could continue to simplify the radical to get 245–√
.

Answer 1

To simplify \(4\sqrt{5} \cdot 2\sqrt{3}\), we multiply the coefficients and the radicals separately.

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

2. Multiply the radicals: \[ \sqrt{5} \cdot \sqrt{3} = \sqrt{5 \cdot 3} = \sqrt{15} \]

Putting it together, we have: \[ 4\sqrt{5} \cdot 2\sqrt{3} = 8\sqrt{15} \]

Therefore, Sandra's final answer of \(8\sqrt{15}\) is indeed correct.

So the answer is: A. Sandra's simplified answer is correct.