To simplify [tex]\(\sqrt{\frac{7}{100}}\)[/tex] using the quotient rule, let's follow these steps:
1. Understand the Quotient Rule for Square Roots:
The quotient rule states that:
[tex]\[
\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}
\][/tex]
This means we can split the square root of a fraction into the square root of the numerator divided by the square root of the denominator.
2. Identify the Numerator and Denominator:
In the expression [tex]\(\sqrt{\frac{7}{100}}\)[/tex]:
- The numerator ([tex]\(a\)[/tex]) is 7.
- The denominator ([tex]\(b\)[/tex]) is 100.
3. Find the Square Root of the Numerator:
[tex]\[
\sqrt{7} \approx 2.6457513110645907
\][/tex]
4. Find the Square Root of the Denominator:
[tex]\[
\sqrt{100} = 10
\][/tex]
5. Apply the Quotient Rule:
Using the quotient rule, we can now write:
[tex]\[
\sqrt{\frac{7}{100}} = \frac{\sqrt{7}}{\sqrt{100}} = \frac{2.6457513110645907}{10} \approx 0.2645751311064591
\][/tex]
So, by applying the quotient rule to [tex]\(\sqrt{\frac{7}{100}}\)[/tex], we have:
[tex]\[
\sqrt{\frac{7}{100}} = 0.2645751311064591
\][/tex]
From our calculations, the simplified form of [tex]\(\sqrt{\frac{7}{100}}\)[/tex] is approximately [tex]\(0.2645751311064591\)[/tex].
