What is \sqrt[3]{\sqrt[4]{64}} ?

The solution to \sqrt[3]{\sqrt[4]{64}} is square root of 2

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simplify \sqrt[3]{\sqrt[4]{64}}

simplify

2

Decimal Notation

1.41421 \dots

Solution steps

Apply radical rule:

= 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2^{\frac{1}{3}} \cdot 2^{\frac{1}{6}} = 2^{\frac{1}{3} + \frac{1}{6}}

= 2^{\frac{1}{3} + \frac{1}{6}}

\frac{1}{3} + \frac{1}{6} = \frac{1}{2}

= 2^{\frac{1}{2}}

Apply exponent rule:

a^{\frac{1}{2}} = a

2^{\frac{1}{2}} = 2

= 2

((x - 5)^{\frac{3}{2}})^{\frac{2}{3}}

7 x^{2} y^{2}

\frac{( - 6 ) ^{3}}{2 ^{3}}

What is \sqrt[3]{\sqrt[4]{64}} ?
The solution to \sqrt[3]{\sqrt[4]{64}} is square root of 2