Question

Simplify the following radical expressions.



(2 points)
72−−√
=

Answer 1

To simplify the radical expression \(\sqrt{72}\), we start by finding the prime factorization of 72.

1. The prime factorization of 72 is:
\[
72 = 2^3 \times 3^2
\]

2. Now we use the property of square roots, which states that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):
\[
\sqrt{72} = \sqrt{2^3 \times 3^2}
\]

3. We can separate the square roots:
\[
\sqrt{72} = \sqrt{2^2 \times 2^1 \times 3^2} = \sqrt{(2^2)} \times \sqrt{(3^2)} \times \sqrt{(2^1)}
\]

4. Now, we simplify:
\[
\sqrt{(2^2)} = 2, \quad \sqrt{(3^2)} = 3, \quad \text{and} \quad \sqrt{(2^1)} = \sqrt{2}
\]
Putting it all together:
\[
\sqrt{72} = 2 \times 3 \times \sqrt{2} = 6\sqrt{2}
\]

So, the simplified form of \(\sqrt{72}\) is:
\[
\sqrt{72} = 6\sqrt{2}
\]