Certainly! Let's solve this step by step.
1. Identify two factors of 36 that are perfect squares:
- The number 36 can be factored in various ways, but we need factors that are also perfect squares. Two such factors are 4 and 9, since both 4 and 9 are perfect squares.
2. Rewrite the square root of 36 using these factors:
- We can express [tex]\(\sqrt{36}\)[/tex] as [tex]\(\sqrt{4 \times 9}\)[/tex].
3. Apply the property of square roots:
- The square root of a product can be expressed as the product of the square roots of the factors. So,
[tex]\[
\sqrt{36} = \sqrt{4 \times 9} = \sqrt{4} \times \sqrt{9}
\][/tex]
4. Simplify the square roots:
- Since [tex]\(\sqrt{4} = 2\)[/tex] and [tex]\(\sqrt{9} = 3\)[/tex], we get:
[tex]\[
\sqrt{4} \times \sqrt{9} = 2 \times 3 = 6
\][/tex]
Therefore, [tex]\(\sqrt{36}\)[/tex] can be rewritten as the product of two square roots of perfect squares as:
[tex]\[
\sqrt{36} = \sqrt{4} \times \sqrt{9} = 6
\][/tex]
In summary, the two factors of 36 that are perfect squares are 4 and 9, and the product of their square roots is indeed 6.
