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Answer :
To express [tex]\(\frac{1}{25} h^2\)[/tex] as a perfect square, we need to determine which of the given options can be rewritten as a perfect square.
A perfect square means we can write it in the form of [tex]\(a^2\)[/tex].
Let's examine [tex]\(\frac{1}{25} h^2\)[/tex]:
1. Coefficient Simplification:
The coefficient [tex]\(\frac{1}{25}\)[/tex] can be written as [tex]\(\left(\frac{1}{5}\right)^2\)[/tex]. This is because [tex]\(\left(\frac{1}{5}\right) \times \left(\frac{1}{5}\right) = \frac{1}{25}\)[/tex].
2. Combine with [tex]\(h^2\)[/tex]:
[tex]\(\frac{1}{25} h^2\)[/tex] can be broken down into two parts: [tex]\(\left(\frac{1}{5}\right)^2\)[/tex] and [tex]\(h^2\)[/tex].
3. Form a Single Square:
[tex]\(\left(\frac{1}{5}\right)^2 \times h^2\)[/tex] can be expressed as [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
Therefore, the expression [tex]\(\frac{1}{25} h^2\)[/tex] as a perfect square is [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
This matches the second option: [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
A perfect square means we can write it in the form of [tex]\(a^2\)[/tex].
Let's examine [tex]\(\frac{1}{25} h^2\)[/tex]:
1. Coefficient Simplification:
The coefficient [tex]\(\frac{1}{25}\)[/tex] can be written as [tex]\(\left(\frac{1}{5}\right)^2\)[/tex]. This is because [tex]\(\left(\frac{1}{5}\right) \times \left(\frac{1}{5}\right) = \frac{1}{25}\)[/tex].
2. Combine with [tex]\(h^2\)[/tex]:
[tex]\(\frac{1}{25} h^2\)[/tex] can be broken down into two parts: [tex]\(\left(\frac{1}{5}\right)^2\)[/tex] and [tex]\(h^2\)[/tex].
3. Form a Single Square:
[tex]\(\left(\frac{1}{5}\right)^2 \times h^2\)[/tex] can be expressed as [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
Therefore, the expression [tex]\(\frac{1}{25} h^2\)[/tex] as a perfect square is [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
This matches the second option: [tex]\(\left(\frac{1}{5} h\right)^2\)[/tex].
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