What is sqrt(\sqrt[3]{343)} ?

The solution to sqrt(\sqrt[3]{343)} is square root of 7

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simplify sqrt(\sqrt[3]{343)}

simplify

7

Decimal Notation

2.64575 \dots

Solution steps

Apply radical rule:

= (34 3^{\frac{1}{3}})^{\frac{1}{2}}

Apply exponent rule:

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

= 34 3^{\frac{1}{3} \cdot \frac{1}{2}}

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

= 34 3^{\frac{1}{6}}

Factor the number:

343 = 7^{3}

Apply exponent rule:

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

= 7

4905 (7.854 \cdot 1 0^{- 3})

m n

0.53 \cdot 1 0^{- 10} \cdot 16 \cdot 2 π

0.01 \cdot e^{- 23.6}

(18 e^{- 3 t}) (2 e^{3 t} + 6 e^{3 t} t)

What is sqrt(\sqrt[3]{343)} ?
The solution to sqrt(\sqrt[3]{343)} is square root of 7