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Popular >

simplify 3sqrt(\sqrt{27)}

Solution

simplify

327

Solution

+1

Decimal Notation

6.83852 \dots

Solution steps

327

27 = 33

= 333

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

33 = 33

= 333

Apply radical rule:

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

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

\frac{1}{2} + \frac{1}{4} = \frac{3}{4}

= 3 \cdot 3^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is 3sqrt(\sqrt{27)} ?
The solution to 3sqrt(\sqrt{27)} is 3\sqrt[4]{3^3}