Simplify 252−−−√

Question

(1 point)
Responses

1221−−√
12 square root of 21

67–√
6 square root of 7

328−−√
3 square root of 28

263−−√
2 square root of 63

Answer 1

To simplify \( \sqrt{252} \):

1. First, we can factor 252 into its prime factors: \[ 252 = 2^2 \times 3^2 \times 7 \]

2. Next, we can use the properties of square roots: \[ \sqrt{252} = \sqrt{2^2 \times 3^2 \times 7} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{7} = 2 \times 3 \times \sqrt{7} \]

3. Simplifying gives us: \[ 6\sqrt{7} \]

So the simplified form of \( \sqrt{252} \) is \( 6\sqrt{7} \).

The correct response is: \( 6\sqrt{7} \).