What is sqrt(\sqrt{\sqrt{64)}} ?

The solution to sqrt(\sqrt{\sqrt{64)}} is \sqrt[4]{2^3}

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simplify sqrt(\sqrt{\sqrt{64)}}

simplify

64

Decimal Notation

1.68179 \dots

Solution steps

64

64 = 22

= 22

Apply radical rule:

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

22 = 22

= 22

Apply radical rule:

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

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

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

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

2.5 \cdot 1 0^{- 7}

(x)

1^{2} e^{- 1}

400 e^{- 0.0244 (40)}

(7 - 2) (7 - 2)

What is sqrt(\sqrt{\sqrt{64)}} ?
The solution to sqrt(\sqrt{\sqrt{64)}} is \sqrt[4]{2^3}