We need to find the square root of 576, i.e., we need to find the value of $\sqrt{576}$.

1. Problem Description

We need to find the square root of 576, i.e., we need to find the value of $\sqrt{576}$.

2. Solution Steps

We can find the square root of 576 by prime factorization.

First, we find the prime factorization of

5

7

6. $576 = 2 \times 288$

$576 = 2 \times 2 \times 144$

$576 = 2 \times 2 \times 12 \times 12$

$576 = 2 \times 2 \times (2 \times 2 \times 3) \times (2 \times 2 \times 3)$

$576 = 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 2 \times 3$

$576 = 2^6 \times 3^2$

$\sqrt{576} = \sqrt{2^6 \times 3^2} = \sqrt{2^6} \times \sqrt{3^2} = (2^6)^{1/2} \times (3^2)^{1/2} = 2^{6/2} \times 3^{2/2} = 2^3 \times 3^1 = 8 \times 3 = 24$

Alternatively, since we know that $576 = 2 \times 2 \times 12 \times 12$,

$576 = 4 \times 144 = 4 \times 12 \times 12$

$576 = 2^2 \times 12^2$

$\sqrt{576} = \sqrt{2^2 \times 12^2} = \sqrt{2^2} \times \sqrt{12^2} = 2 \times 12 = 24$

We can also directly test some integers to find the square root.

$20^2 = 400$

$25^2 = 625$

Since 576 is between 400 and 625, the square root of 576 is between 20 and

2

5. Try 24: $24 \times 24 = 576$.

3. Final Answer

24