1. **State the problem:** Find the square root of 175. 2. **Formula and rules:** The square root of a number $x$ is a value $y$ such that $$y^2 = x.$$ We can simplify square roots by factoring out perfect squares. 3. **Factorize 175:** $$175 = 25 \times 7$$ 4. **Simplify the square root:** $$\sqrt{175} = \sqrt{25 \times 7} = \sqrt{25} \times \sqrt{7}$$ 5. **Evaluate the perfect square root:** $$\sqrt{25} = 5$$ 6. **Final simplified form:** $$\sqrt{175} = 5\sqrt{7}$$ **Answer:** The square root of 175 simplified is $5\sqrt{7}$.