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Popular >

simplify sqrt(\sqrt[3]{81)}

Solution

simplify

Solution

+1

Decimal Notation

2.08008 \dots

Solution steps

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

Apply radical rule:

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

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

= 3^{\frac{2}{3}}

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt[3]{81)} ?
The solution to sqrt(\sqrt[3]{81)} is cube root of 3^2