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Popular >

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

Solution

simplify

Solution

3

+1

Decimal Notation

1.73205 \dots

Solution steps

Apply radical rule:

Apply radical rule:

Apply radical rule:

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

Apply exponent rule:

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

3^{\frac{1}{3}} \cdot 3^{\frac{1}{6}} = 3^{\frac{1}{3} + \frac{1}{6}}

= 3^{\frac{1}{3} + \frac{1}{6}}

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

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

Apply exponent rule:

a^{\frac{1}{2}} = a

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

= 3

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Frequently Asked Questions (FAQ)

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