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Answer :
Let's solve each part of the question step-by-step.
### Part A:
We need to evaluate the expression [tex]\(\sqrt{\frac{1}{25}}\)[/tex].
1. Identify the Numerator and Denominator:
- The numerator is 1.
- The denominator is 25.
2. Take the Square Root of the Numerator and Denominator:
- The square root of 1 is 1, because [tex]\(1 \times 1 = 1\)[/tex].
- The square root of 25 is 5, because [tex]\(5 \times 5 = 25\)[/tex].
3. Form the Fraction:
- The result of [tex]\(\sqrt{\frac{1}{25}}\)[/tex] is [tex]\(\frac{1}{5}\)[/tex].
So, the answer for part A is [tex]\(\frac{1}{5}\)[/tex].
### Part B:
We need to evaluate the expression [tex]\(-\sqrt{\frac{1}{25}}\)[/tex].
1. Already Evaluated:
- We already know from part A that [tex]\(\sqrt{\frac{1}{25}} = \frac{1}{5}\)[/tex].
2. Apply the Negative Sign:
- By adding the negative sign in front of [tex]\(\frac{1}{5}\)[/tex], we get [tex]\(-\frac{1}{5}\)[/tex].
So, the answer for part B is [tex]\(-\frac{1}{5}\)[/tex].
In summary, the results are:
A) [tex]\(\sqrt{\frac{1}{25}} = \frac{1}{5}\)[/tex]
B) [tex]\(-\sqrt{\frac{1}{25}} = -\frac{1}{5}\)[/tex]
### Part A:
We need to evaluate the expression [tex]\(\sqrt{\frac{1}{25}}\)[/tex].
1. Identify the Numerator and Denominator:
- The numerator is 1.
- The denominator is 25.
2. Take the Square Root of the Numerator and Denominator:
- The square root of 1 is 1, because [tex]\(1 \times 1 = 1\)[/tex].
- The square root of 25 is 5, because [tex]\(5 \times 5 = 25\)[/tex].
3. Form the Fraction:
- The result of [tex]\(\sqrt{\frac{1}{25}}\)[/tex] is [tex]\(\frac{1}{5}\)[/tex].
So, the answer for part A is [tex]\(\frac{1}{5}\)[/tex].
### Part B:
We need to evaluate the expression [tex]\(-\sqrt{\frac{1}{25}}\)[/tex].
1. Already Evaluated:
- We already know from part A that [tex]\(\sqrt{\frac{1}{25}} = \frac{1}{5}\)[/tex].
2. Apply the Negative Sign:
- By adding the negative sign in front of [tex]\(\frac{1}{5}\)[/tex], we get [tex]\(-\frac{1}{5}\)[/tex].
So, the answer for part B is [tex]\(-\frac{1}{5}\)[/tex].
In summary, the results are:
A) [tex]\(\sqrt{\frac{1}{25}} = \frac{1}{5}\)[/tex]
B) [tex]\(-\sqrt{\frac{1}{25}} = -\frac{1}{5}\)[/tex]
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