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Popular >

simplify sqrt(\sqrt[3]{27)}

Solution

simplify

Solution

3

+1

Decimal Notation

1.73205 \dots

Solution steps

Apply radical rule:

= (2 7^{\frac{1}{3}})^{\frac{1}{2}}

Apply exponent rule:

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

= 2 7^{\frac{1}{3} \cdot \frac{1}{2}}

\frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6}

= 2 7^{\frac{1}{6}}

Factor the number:

27 = 3^{3}

Apply exponent rule:

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

= 3

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt[3]{27)} ?
The solution to sqrt(\sqrt[3]{27)} is square root of 3