Question

Simplify the radical expression. $$\sqrt{175}$$

Short answer

The simplified form of \(\sqrt{175}\) is \(5 \sqrt{7}\).

Step-by-step solution

Prime factorization of 175

Start by finding the prime factorization of 175. This can be done by repeatedly dividing by prime numbers. The prime factors of 175 are \(5^2 \times 7\). So, the factorization will be 175 = \(5^2 \times 7\).

Use property of square roots

One of the properties of square roots says that \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\). Apply this property to the square root of \(5^2 \times 7\) to get \(\sqrt{175} = \sqrt{5^2} \times \sqrt{7}\).

Simplify the square root

Finally, simplify the square root of \(5^2\) and that will result in 5, resulting in the simplified radical expression \(\sqrt{175} = 5 \sqrt{7}\).