Simplify 252−−−√

Question

(1 point)
Responses

67–√
6 square root of 7

328−−√
3 square root of 28

1221−−√
12 square root of 21

263−−√

Answer 1

To simplify \( \sqrt{252} \), we can factor the number under the square root into its prime factors:

1. First, find the prime factorization of 252: \[ 252 = 2^2 \times 3^2 \times 7 \]

2. Now, take the square root: \[ \sqrt{252} = \sqrt{2^2 \times 3^2 \times 7} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{7} = 2 \times 3 \times \sqrt{7} \]

3. Calculate the product: \[ 2 \times 3 = 6 \] Therefore, \[ \sqrt{252} = 6\sqrt{7} \]

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