Let's simplify the expression [tex]\(-\sqrt{\frac{100}{49}}\)[/tex].
1. Expression Inside the Square Root:
[tex]\[
\frac{100}{49}
\][/tex]
2. Simplify the Fraction:
The fraction [tex]\(\frac{100}{49}\)[/tex] in its simplest form stays the same since both numerator (100) and denominator (49) are already in their lowest terms.
3. Taking the Square Root:
Next, we take the square root of both the numerator and the denominator separately:
[tex]\[
\sqrt{\frac{100}{49}} = \frac{\sqrt{100}}{\sqrt{49}}
\][/tex]
4. Calculate the Square Roots:
- The square root of 100 is 10 because [tex]\(10 \times 10 = 100\)[/tex].
- The square root of 49 is 7 because [tex]\(7 \times 7 = 49\)[/tex].
5. Fraction after Simplifying Square Roots:
[tex]\[
\frac{\sqrt{100}}{\sqrt{49}} = \frac{10}{7}
\][/tex]
6. Incorporate the Negative Sign:
Since the original expression is [tex]\(-\sqrt{\frac{100}{49}}\)[/tex], we need to apply the negative sign to our simplified result:
[tex]\[
-\sqrt{\frac{100}{49}} = -\frac{10}{7}
\][/tex]
Therefore, the simplified form of the given radical expression is:
[tex]\[
-\frac{10}{7}
\][/tex]
Among the multiple-choice options given, the correct one is:
[tex]\[
-\frac{10}{7}
\][/tex]
