Simplify 252−−−√

Question

(1 point)
Responses

263−−√
2 square root of 63

1221−−√
12 square root of 21

67–√
6 square root of 7

328−−√

Answer 1

To simplify \( \sqrt{252} \), we can factor 252 into its prime factors:

1. The prime factorization of 252 is: \[ 252 = 2^2 \times 3^2 \times 7 \]

2. Using properties of square roots: \[ \sqrt{252} = \sqrt{(2^2) \times (3^2) \times 7} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{7} \]

3. Simplifying each part gives: \[ \sqrt{2^2} = 2, \quad \sqrt{3^2} = 3 \]

4. Therefore, \[ \sqrt{252} = 2 \times 3 \times \sqrt{7} = 6\sqrt{7} \]

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

So, the correct response is:

• \( 6\sqrt{7} \)