To simplify the square root [tex]\(\sqrt{\frac{16}{25}}\)[/tex], let's break it down step-by-step.
1. Recognize that the square root of a fraction can be rewritten as the square root of the numerator divided by the square root of the denominator:
[tex]\[ \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} \][/tex]
2. Calculate the square root of the numerator (16) and the denominator (25) individually:
- The square root of 16 is 4 because [tex]\(4 \times 4 = 16\)[/tex].
- The square root of 25 is 5 because [tex]\(5 \times 5 = 25\)[/tex].
3. Substitute these values back into the fraction:
[tex]\[ \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5} \][/tex]
4. Therefore, the simplified form of the square root [tex]\(\sqrt{\frac{16}{25}}\)[/tex] is:
[tex]\[ \sqrt{\frac{16}{25}} = \frac{4}{5} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\frac{4}{5}} \][/tex]
