What is sqrt(\sqrt[3]{\sqrt[5]{5^{25)}}} ?

The solution to sqrt(\sqrt[3]{\sqrt[5]{5^{25)}}} is \sqrt[6]{5^5}

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simplify sqrt(\sqrt[3]{\sqrt[5]{5^{25)}}}

simplify

Decimal Notation

3.82362 \dots

Solution steps

Apply radical rule:

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

Apply radical rule:

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

5 = 5^{\frac{1}{2}}

Apply radical rule:

= 5^{\frac{1}{2}} \cdot 5^{\frac{1}{3}}

Apply exponent rule:

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

5^{\frac{1}{2}} \cdot 5^{\frac{1}{3}} = 5^{\frac{1}{2} + \frac{1}{3}}

= 5^{\frac{1}{2} + \frac{1}{3}}

\frac{1}{2} + \frac{1}{3} = \frac{5}{6}

= 5^{\frac{5}{6}}

e^{- x^{3}} \cdot (- \frac{1}{3}) e^{- x^{3}}

(e^{l n (2)})^{2}

(3 x^{3}) (7 x^{10}) (5 x^{6})

6.023 \cdot 1 0^{23} (6.626 \cdot 1 0^{- 34}) (3 \cdot 1 0^{8})

(\frac{1}{10} mn) (\frac{4}{9} mn) (\frac{9}{4} m n^{3})

What is sqrt(\sqrt[3]{\sqrt[5]{5^{25)}}} ?
The solution to sqrt(\sqrt[3]{\sqrt[5]{5^{25)}}} is \sqrt[6]{5^5}