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Popular >

simplify sqrt(\sqrt{2\sqrt{2)}}

Solution

simplify

22

Solution

2^{\frac{3}{8}}

+1

Solution steps

22

Apply radical rule:

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

= ((22)^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

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

= (22)^{\frac{1}{2} \cdot \frac{1}{2}}

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

= (22)^{\frac{1}{4}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

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

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

Join

\frac{1}{4} + \frac{1}{8} : \frac{3}{8}

= 2^{\frac{3}{8}}

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Frequently Asked Questions (FAQ)

What is sqrt(\sqrt{2\sqrt{2)}} ?
The solution to sqrt(\sqrt{2\sqrt{2)}} is 2^{3/8}