What is \sqrt[5]{sqrt(3*\sqrt{2)}} ?

The solution to \sqrt[5]{sqrt(3*\sqrt{2)}} is \sqrt[10]{3}\sqrt[20]{2}

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simplify \sqrt[5]{sqrt(3*\sqrt{2)}}

simplify

Decimal Notation

1.15548 \dots

Solution steps

Apply radical rule:

= ((32)^{\frac{1}{2}})^{\frac{1}{5}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (32)^{\frac{1}{2} \cdot \frac{1}{5}}

\frac{1}{2} \cdot \frac{1}{5} = \frac{1}{10}

= (32)^{\frac{1}{10}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

4 π sin (2 π rs t^{3}) 4 s^{2} t (t^{3}) cos (2 π s t^{3})

- (x e^{- x^{2}})

2 (5.67 \cdot 1 0^{- 8}) (266.32)^{4}

x^{3} (2 x^{2})

6.94 \cdot 1 0^{- 3}

What is \sqrt[5]{sqrt(3*\sqrt{2)}} ?
The solution to \sqrt[5]{sqrt(3*\sqrt{2)}} is \sqrt[10]{3}\sqrt[20]{2}