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Answer :
To express [tex]\(\frac{1}{25} h^2\)[/tex] as a perfect square, we want to write it in the form [tex]\((x)^2\)[/tex] for some expression [tex]\(x\)[/tex].
Let's break it down step-by-step:
1. We have the expression [tex]\(\frac{1}{25} h^2\)[/tex].
2. Notice that [tex]\(\frac{1}{25}\)[/tex] is actually [tex]\((\frac{1}{5})^2\)[/tex]. This is because if you square [tex]\(\frac{1}{5}\)[/tex], you get [tex]\(\frac{1}{5} \times \frac{1}{5} = \frac{1}{25}\)[/tex].
3. The expression [tex]\(h^2\)[/tex] is already a perfect square since it's [tex]\((h)^2\)[/tex].
4. Combining both of these insights, the entire expression [tex]\(\frac{1}{25} h^2\)[/tex] can be rewritten as:
[tex]\[
\left(\frac{1}{5} \times h\right)^2
\][/tex]
5. Therefore, the perfect square expression is [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
The correct option that matches this expression is:
[tex]\[
\left(\frac{1}{5} h\right)^2
\][/tex]
Let's break it down step-by-step:
1. We have the expression [tex]\(\frac{1}{25} h^2\)[/tex].
2. Notice that [tex]\(\frac{1}{25}\)[/tex] is actually [tex]\((\frac{1}{5})^2\)[/tex]. This is because if you square [tex]\(\frac{1}{5}\)[/tex], you get [tex]\(\frac{1}{5} \times \frac{1}{5} = \frac{1}{25}\)[/tex].
3. The expression [tex]\(h^2\)[/tex] is already a perfect square since it's [tex]\((h)^2\)[/tex].
4. Combining both of these insights, the entire expression [tex]\(\frac{1}{25} h^2\)[/tex] can be rewritten as:
[tex]\[
\left(\frac{1}{5} \times h\right)^2
\][/tex]
5. Therefore, the perfect square expression is [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
The correct option that matches this expression is:
[tex]\[
\left(\frac{1}{5} h\right)^2
\][/tex]
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