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Popular >

simplify \sqrt[4]{sqrt(81)}

Solution

simplify

Solution

3

+1

Decimal Notation

1.73205 \dots

Solution steps

Apply radical rule:

= (8 1^{\frac{1}{2}})^{\frac{1}{4}}

Apply exponent rule:

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

= 8 1^{\frac{1}{2} \cdot \frac{1}{4}}

\frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8}

= 8 1^{\frac{1}{8}}

Factor the number:

81 = 3^{4}

Apply exponent rule:

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

= 3

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{sqrt(81)} ?
The solution to \sqrt[4]{sqrt(81)} is square root of 3