Question

Write the radical below in the simplest radical form. Decimals are not allowed.
√175

Answer 1

To simplify \(\sqrt{175}\), factor 175 into its prime factors (5x5x7), then take the square root of the pair of 5s out of the radical, resulting in \(5\sqrt{7}\).

Step-by-step explanation:

To write the radical \(\sqrt{175}\) in the simplest radical form, you first want to factor 175 into its prime factors.

175 can be factored into 5 \times 5 \times 7. Since the square root function looks for pairs of prime factors, the pair of 5s can be taken out from under the radical, leaving the 7 inside. Therefore, \(\sqrt{175}\) simplifies to \(5\sqrt{7}\).

Here are the steps to simplify \(\sqrt{175}\):

1. Factor 175 into its prime factors: 175 = 5 \times 5 \times 7.
2. Pair the prime factors under the square root to simplify: \(\sqrt{175} = \sqrt{5 \times 5 \times 7}\).
3. Take out the pair of 5s, because \(5 \times 5 = 25\), and we know that \(\sqrt{25} = 5\).
4. Write the simplified version: 5\sqrt{7}\.