Question
Simplify the following radical sqrt(180)
Answers
GPT-4o mini
To simplify \(\sqrt{180}\), we start by factoring 180 into its prime factors.
\[
180 = 36 \times 5 = 6^2 \times 5 = (2 \times 3)^2 \times 5
\]
Next, we can express \(\sqrt{180}\) in terms of its factors:
\[
\sqrt{180} = \sqrt{36 \times 5}
\]
Using the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can separate the square root:
\[
\sqrt{180} = \sqrt{36} \times \sqrt{5}
\]
Since \(\sqrt{36} = 6\), we have:
\[
\sqrt{180} = 6 \times \sqrt{5}
\]
Therefore, the simplified form of \(\sqrt{180}\) is:
\[
\boxed{6\sqrt{5}}
\]
\[
180 = 36 \times 5 = 6^2 \times 5 = (2 \times 3)^2 \times 5
\]
Next, we can express \(\sqrt{180}\) in terms of its factors:
\[
\sqrt{180} = \sqrt{36 \times 5}
\]
Using the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can separate the square root:
\[
\sqrt{180} = \sqrt{36} \times \sqrt{5}
\]
Since \(\sqrt{36} = 6\), we have:
\[
\sqrt{180} = 6 \times \sqrt{5}
\]
Therefore, the simplified form of \(\sqrt{180}\) is:
\[
\boxed{6\sqrt{5}}
\]