To determine the value of [tex]\(\sqrt[3]{\sqrt{64}}\)[/tex], we need to break it down into two main steps: calculating the square root of 64 and then finding the cube root of that result.
1. Calculate [tex]\(\sqrt{64}\)[/tex]:
The square root of 64 is the number which, when multiplied by itself, gives the product 64. In this case:
[tex]\[
\sqrt{64} = 8
\][/tex]
2. Calculate [tex]\(\sqrt[3]{8}\)[/tex]:
Now, we need to find the cube root of 8. The cube root of 8 is the number which, when raised to the power of 3, gives the product 8. In this case:
[tex]\[
\sqrt[3]{8} = 2
\][/tex]
Therefore, the value of [tex]\(\sqrt[3]{\sqrt{64}}\)[/tex] is [tex]\(2\)[/tex].
[tex]\[
\boxed{2}
\][/tex]
