simplify the square root of 175.

√175 = √25 * √7

= 5√7

To simplify the square root of 175, you need to find the largest perfect square that divides evenly into 175.

Start by finding the prime factorization of 175:

175 = 5 × 5 × 7

Now, look for pairs of matching prime factors:

5 × 5 × 7

Since there are two 5's, you can simplify them as one square root:

√(5 × 5 × 7) = 5√7

Therefore, the simplified square root of 175 is 5√7.