The problem is to find the square root of 504, i.e., to calculate $\sqrt{504}$.

1. Problem Description

The problem is to find the square root of 504, i.e., to calculate $\sqrt{504}$.

2. Solution Steps

We want to simplify $\sqrt{504}$. We can do this by finding the prime factorization of

5

0

4. $504 = 2 \times 252 = 2 \times 2 \times 126 = 2 \times 2 \times 2 \times 63 = 2^3 \times 63 = 2^3 \times 3 \times 21 = 2^3 \times 3 \times 3 \times 7 = 2^3 \times 3^2 \times 7$.

Therefore, $504 = 2^3 \times 3^2 \times 7 = 2^2 \times 2 \times 3^2 \times 7 = 2^2 \times 3^2 \times (2 \times 7) = 4 \times 9 \times 14 = 36 \times 14$.

Then, we have

$\sqrt{504} = \sqrt{2^3 \times 3^2 \times 7} = \sqrt{2^2 \times 2 \times 3^2 \times 7} = \sqrt{2^2 \times 3^2 \times 2 \times 7} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{14} = 2 \times 3 \times \sqrt{14} = 6\sqrt{14}$.

3. Final Answer

The square root of 504 is $6\sqrt{14}$.