Simply by factoring square root of 175

In order to simplify √175, I will use the branch-off method. It is where you take two smaller numbers that multiply up to 175.

175 = 5 x 35

35 = 5 x 7

At the end of the branch, we get 5, 5, and 7. Put any duplicate numbers outside the square root symbol and the rest back inside.

The answer is 5√7