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Answer :
We want to simplify the expression:
[tex]$$
\sqrt{\frac{1}{25}}.
$$[/tex]
Step 1: Express the square root of the fraction as the fraction of square roots. For any non-negative numbers [tex]$a$[/tex] and [tex]$b$[/tex], we have:
[tex]$$
\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}.
$$[/tex]
Step 2: Apply this property with [tex]$a = 1$[/tex] and [tex]$b = 25$[/tex]:
[tex]$$
\sqrt{\frac{1}{25}} = \frac{\sqrt{1}}{\sqrt{25}}.
$$[/tex]
Step 3: Compute [tex]$\sqrt{1}$[/tex] and [tex]$\sqrt{25}$[/tex]. Since [tex]$\sqrt{1} = 1$[/tex] and [tex]$\sqrt{25} = 5$[/tex], the expression becomes:
[tex]$$
\frac{\sqrt{1}}{\sqrt{25}} = \frac{1}{5}.
$$[/tex]
Thus, the simplified result is:
[tex]$$
\sqrt{\frac{1}{25}} = \frac{1}{5}.
$$[/tex]
So the correct choice is:
A. [tex]$\sqrt{\frac{1}{25}} = \frac{1}{5}$[/tex]
[tex]$$
\sqrt{\frac{1}{25}}.
$$[/tex]
Step 1: Express the square root of the fraction as the fraction of square roots. For any non-negative numbers [tex]$a$[/tex] and [tex]$b$[/tex], we have:
[tex]$$
\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}.
$$[/tex]
Step 2: Apply this property with [tex]$a = 1$[/tex] and [tex]$b = 25$[/tex]:
[tex]$$
\sqrt{\frac{1}{25}} = \frac{\sqrt{1}}{\sqrt{25}}.
$$[/tex]
Step 3: Compute [tex]$\sqrt{1}$[/tex] and [tex]$\sqrt{25}$[/tex]. Since [tex]$\sqrt{1} = 1$[/tex] and [tex]$\sqrt{25} = 5$[/tex], the expression becomes:
[tex]$$
\frac{\sqrt{1}}{\sqrt{25}} = \frac{1}{5}.
$$[/tex]
Thus, the simplified result is:
[tex]$$
\sqrt{\frac{1}{25}} = \frac{1}{5}.
$$[/tex]
So the correct choice is:
A. [tex]$\sqrt{\frac{1}{25}} = \frac{1}{5}$[/tex]
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