What is \sqrt[4]{\sqrt[3]{125}} ?

The solution to \sqrt[4]{\sqrt[3]{125}} is \sqrt[4]{5}

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simplify \sqrt[4]{\sqrt[3]{125}}

simplify

Decimal Notation

1.49534 \dots

Solution steps

Apply radical rule:

= (12 5^{\frac{1}{3}})^{\frac{1}{4}}

Apply exponent rule:

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

= 12 5^{\frac{1}{3} \cdot \frac{1}{4}}

\frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}

= 12 5^{\frac{1}{12}}

Factor the number:

125 = 5^{3}

Apply exponent rule:

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

e^{- x} \times x

e^{- 4.56}

cos (x) \cdot e^{- x^{2}}

e^{- x c s c (x)}

(x - 5)^{3}

What is \sqrt[4]{\sqrt[3]{125}} ?
The solution to \sqrt[4]{\sqrt[3]{125}} is \sqrt[4]{5}