The question is given to be:
[tex]\sqrt[]{\frac{64}{100}}[/tex]
Recall the rule:
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]
Therefore, the expression becomes:
[tex]\sqrt[]{\frac{64}{100}}=\frac{\sqrt[]{64}}{\sqrt[]{100}}[/tex]
Recall that:
[tex]\begin{gathered} 8\times8=64,\therefore\sqrt[]{64}=8 \\ \text{and} \\ 10\times10=100,\therefore\sqrt[]{100}=10 \end{gathered}[/tex]
Hence, the expression becomes:
[tex]\frac{\sqrt[]{64}}{\sqrt[]{100}}=\frac{8}{10}[/tex]
Dividing through by 2, we have:
[tex]\frac{8}{10}=\frac{4}{5}[/tex]
Therefore, the answer is:
[tex]\sqrt[]{\frac{64}{100}}=\frac{4}{5}[/tex]
