simplify square root 75

1 answer

To simplify \(\sqrt{75}\), we can factor 75 into its prime factors:

\[ 75 = 25 \times 3 = 5^2 \times 3 \]

Now, we can use the property of square roots that says \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):

\[ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} \]

Since \(\sqrt{25} = 5\), we have:

\[ \sqrt{75} = 5 \times \sqrt{3} \]

Thus, the simplified form of \(\sqrt{75}\) is:

\[ 5\sqrt{3} \]