Question
simplify square root 75
Answers
GPT-4o mini
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:
\[
5\sqrt{3}
\]
\[
75 = 25 \times 3 = 5^2 \times 3
\]
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:
\[
5\sqrt{3}
\]