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[tex]\[
\begin{array}{l}
\sqrt{\frac{100}{121}} = \frac{10}{11} \\
\sqrt[3]{\frac{27}{512}} = \frac{3}{8} \\
\sqrt[4]{\frac{16}{81}} = \frac{2}{3} \\
\sqrt{\frac{169}{225}} = \frac{13}{15} \\
\sqrt[6]{\frac{1}{64}} = \frac{1}{2} \\
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's solve each of the given expressions step by step.

1. Correcting the given expression: The first expression [tex]\( \sqrt{\frac{100}{121}} = -10 \)[/tex] is incorrect. The square root of a fraction cannot be negative if it's derived from positive real numbers. The correct square root of [tex]\(\frac{100}{121}\)[/tex] should be:
[tex]\[ \sqrt{\frac{100}{121}} = \sqrt{\frac{10^2}{11^2}} = \frac{10}{11} \][/tex]

2. Cube root of [tex]\(\frac{27}{512}\)[/tex]:
[tex]\[ \sqrt[3]{\frac{27}{512}} = 0.375 \][/tex]

3. Fourth root of [tex]\(\frac{16}{81}\)[/tex]:
[tex]\[ \sqrt[4]{\frac{16}{81}} = 0.6666666666666666 \][/tex]

4. Square root of [tex]\(\frac{169}{225}\)[/tex]:
[tex]\[ \sqrt{\frac{169}{225}} = 0.8666666666666666 \][/tex]

5. Sixth root of [tex]\(\frac{1}{64}\)[/tex]:
[tex]\[ \sqrt[6]{\frac{1}{64}} = 0.5 \][/tex]

So, the detailed step-by-step solution provides the following results for each expression:

[tex]\[ \sqrt[3]{\frac{27}{512}} = 0.375 \][/tex]
[tex]\[ \sqrt[4]{\frac{16}{81}} = 0.6666666666666666 \][/tex]
[tex]\[ \sqrt{\frac{169}{225}} = 0.8666666666666666 \][/tex]
[tex]\[ \sqrt[6]{\frac{1}{64}} = 0.5 \][/tex]
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