To simplify the radical expression [tex]\(\sqrt{\frac{121}{25}}\)[/tex], follow these steps:
1. Identify the components of the fraction inside the square root:
- The numerator is 121.
- The denominator is 25.
2. Break down the square root of a fraction into the square roots of the numerator and the denominator:
[tex]\[
\sqrt{\frac{121}{25}} = \frac{\sqrt{121}}{\sqrt{25}}
\][/tex]
3. Find the square root of the numerator (121):
- [tex]\(\sqrt{121} = 11\)[/tex]
4. Find the square root of the denominator (25):
- [tex]\(\sqrt{25} = 5\)[/tex]
5. Substitute these square roots back into the fraction:
[tex]\[
\frac{\sqrt{121}}{\sqrt{25}} = \frac{11}{5}
\][/tex]
Hence, the simplified form of [tex]\(\sqrt{\frac{121}{25}}\)[/tex] is [tex]\(\frac{11}{5}\)[/tex]. Therefore, the correct answer is:
[tex]\[
\frac{11}{5}
\][/tex]
