What is sqrt(\sqrt{\sqrt{\sqrt{\sqrt{2)}}}} ?

The solution to sqrt(\sqrt{\sqrt{\sqrt{\sqrt{2)}}}} is \sqrt[32]{2}

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

simplify

2

Decimal Notation

1.02189 \dots

Solution steps

2

Apply radical rule:

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

Apply exponent rule:

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

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

Apply radical rule:

Apply exponent rule:

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

\frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8}

Apply radical rule:

= (2^{\frac{1}{4}})^{\frac{1}{8}}

Apply exponent rule:

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

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

\frac{1}{4} \cdot \frac{1}{8} = \frac{1}{32}

= 2^{\frac{1}{32}}

e^{- t} \cdot u (t)

e^{- l n ∣ y^{2} - 1 ∣}

e^{- 0.12 \cdot \frac{3}{12}} (0.6523 \cdot 0 + (1 - 0.6523) \cdot 2.4)

a^{m} b^{m}

(x - 1)^{2} (x - 4)^{2}

What is sqrt(\sqrt{\sqrt{\sqrt{\sqrt{2)}}}} ?
The solution to sqrt(\sqrt{\sqrt{\sqrt{\sqrt{2)}}}} is \sqrt[32]{2}