What is \sqrt[3]{\sqrt[4]{3^5*3}} ?

The solution to \sqrt[3]{\sqrt[4]{3^5*3}} is square root of 3

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simplify \sqrt[3]{\sqrt[4]{3^5*3}}

simplify

3

Decimal Notation

1.73205 \dots

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

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

= 3

8.854 \cdot 1 0^{- 12} \cdot \frac{35 \cdot 1 0 ^{- 4}}{0.003}

(4 \cdot 1 0^{8}) (2.1 \cdot 1 0^{5})

e^{- 0.01} \cdot e^{- 0.01}

3.911 e^{- 2}

0.8 \cdot 1200 \cdot 1 0^{- 6}

What is \sqrt[3]{\sqrt[4]{3^5*3}} ?
The solution to \sqrt[3]{\sqrt[4]{3^5*3}} is square root of 3