Sure, let's simplify \(\sqrt{72}\) step by step.
1. Start by factoring the number inside the square root:
- 72 can be factored into 36 and 2. This gives us:
[tex]\[
72 = 36 \times 2
\][/tex]
2. Apply the property of square roots:
- The property of square roots tells us that the square root of a product is the product of the square roots. Thus:
[tex]\[
\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2}
\][/tex]
3. Simplify the square roots:
- The square root of 36 is 6 because \( 6 \times 6 = 36 \). So:
[tex]\[
\sqrt{36} = 6
\][/tex]
4. Combine the terms:
- Using the previous results, we have:
[tex]\[
\sqrt{72} = 6 \times \sqrt{2}
\][/tex]
Therefore, the simplest radical form of \(\sqrt{72}\) is:
[tex]\[
6 \times \sqrt{2}
\][/tex]
