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Popular >

simplify \sqrt[5]{512sqrt(8)}

Solution

simplify

Solution

+1

Decimal Notation

4.28709 \dots

Solution steps

Apply radical rule:

Factor integer

16 = 2^{4}

Apply exponent rule:

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

Refine

Factor integer

8 = 2^{3}

Apply exponent rule:

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

= 2 \cdot 2^{\frac{4}{5}} \cdot 2^{3 \cdot \frac{1}{10}}

Refine

= 2 \cdot 2^{\frac{4}{5}} \cdot 2^{\frac{3}{10}}

Apply exponent rule:

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

2 \cdot 2^{\frac{4}{5}} \cdot 2^{\frac{3}{10}} = 2^{1 + \frac{4}{5} + \frac{3}{10}}

= 2^{1 + \frac{4}{5} + \frac{3}{10}}

Join

1 + \frac{4}{5} + \frac{3}{10} : \frac{21}{10}

= 2^{\frac{21}{10}}

2^{\frac{21}{10}} = 2^{2 + \frac{1}{10}}

= 2^{2 + \frac{1}{10}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

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

Refine

2^{2} = 4

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Frequently Asked Questions (FAQ)

What is \sqrt[5]{512sqrt(8)} ?
The solution to \sqrt[5]{512sqrt(8)} is 4\sqrt[10]{2}