Let's solve the problem step by step:
1. Simplify the Fraction Inside the Square Root:
We begin with the expression inside the square root:
[tex]\[
\frac{100}{81}
\][/tex]
2. Calculate the Square Root of the Fraction:
Next, we find the square root of the fraction. Finding the square root of a fraction involves taking the square root of the numerator and the square root of the denominator separately:
[tex]\[
\sqrt{\frac{100}{81}} = \frac{\sqrt{100}}{\sqrt{81}}
\][/tex]
Simplifying the square roots:
[tex]\[
\sqrt{100} = 10
\][/tex]
[tex]\[
\sqrt{81} = 9
\][/tex]
Therefore:
[tex]\[
\sqrt{\frac{100}{81}} = \frac{10}{9}
\][/tex]
3. Negate the Square Root:
To find [tex]\(-\sqrt{\frac{100}{81}}\)[/tex], we simply negate the result obtained from the square root calculation:
[tex]\[
-\sqrt{\frac{100}{81}} = -\frac{10}{9}
\][/tex]
4. Select the Correct Answer:
Comparing our result with the given options:
[tex]\[
-\frac{10}{9}
\][/tex]
We see that option a. matches our result.
Thus, the correct answer is:
a. [tex]\(-10 / 9\)[/tex]
