Sure, let's break down the given problem step by step to understand how to simplify the expression [tex]\(\sqrt{36 y^4}\)[/tex].
1. Identify the expression inside the square root:
[tex]\(\sqrt{36 y^4}\)[/tex]
2. Separate the square root of the product into individual square roots:
According to the property of square roots, [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex], we can rewrite the expression as:
[tex]\[
\sqrt{36 y^4} = \sqrt{36} \cdot \sqrt{y^4}
\][/tex]
3. Simplify [tex]\(\sqrt{36}\)[/tex]:
The square root of 36 is 6 because [tex]\(6 \times 6 = 36\)[/tex]:
[tex]\[
\sqrt{36} = 6
\][/tex]
4. Simplify [tex]\(\sqrt{y^4}\)[/tex]:
The square root of [tex]\(y^4\)[/tex] is [tex]\(y^2\)[/tex] because [tex]\((y^2)^2 = y^4\)[/tex]:
[tex]\[
\sqrt{y^4} = y^2
\][/tex]
5. Combine the results from steps 3 and 4:
Now that we have [tex]\(\sqrt{36} = 6\)[/tex] and [tex]\(\sqrt{y^4} = y^2\)[/tex], multiply these results together:
[tex]\[
6 \cdot y^2
\][/tex]
6. Write the final simplified expression:
[tex]\[
\sqrt{36 y^4} = 6 y^2
\][/tex]
So, the simplified form of the expression [tex]\(\sqrt{36 y^4}\)[/tex] is indeed:
[tex]\[
6 y^2
\][/tex]
This completes the step-by-step simplification.
