Question

Simplify radical 252

A. 12 radical 21
B. 3 radical 28
C. 6 radical 7
D. 2 radical 63

Answer 1

To simplify the radical √252, we need to identify the perfect square factors of 252.

First, we can find the prime factorization of 252:

252 = 2 × 2 × 3 × 3 × 7

Next, we group the prime factors in pairs:

252 = 2 × 2 × (3 × 3) × 7

We can simplify the square root by taking out the perfect square factors:

√252 = √(2 × 2 × (3 × 3) × 7)

Taking the square root of the perfect square factors, we get:

√(2 × 2 × (3 × 3) × 7) = 2 × 3 × √7

Simplifying further, we have:

2 × 3 × √7 = 6√7

Therefore, the simplified form of √252 is 6√7.

Out of the given options, the correct answer is C. 6 radical 7.

Answer 2

To simplify the radical √252, you can first find its prime factorization:

√252 = √(2^2 * 3^2 * 7)

Now, you can take out pairs of factors from under the radical:

√(2^2 * 3^2 * 7) = 2√(3^2 * 7)

= 2 * 3√7

So, the simplified radical √252 is:

B. 6√7