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Popular >

simplify \sqrt[4]{sqrt(5^3)}

Solution

simplify

Solution

+1

Decimal Notation

1.82857 \dots

Solution steps

5^{3} = 55

Apply radical rule:

Apply radical rule:

Apply radical rule:

= 5^{\frac{1}{4}} \cdot 5^{\frac{1}{8}}

Apply exponent rule:

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

5^{\frac{1}{4}} \cdot 5^{\frac{1}{8}} = 5^{\frac{1}{4} + \frac{1}{8}}

= 5^{\frac{1}{4} + \frac{1}{8}}

\frac{1}{4} + \frac{1}{8} = \frac{3}{8}

= 5^{\frac{3}{8}}

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{sqrt(5^3)} ?
The solution to \sqrt[4]{sqrt(5^3)} is \sqrt[8]{5^3}