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

The solution to sqrt(\sqrt{\sqrt{\sqrt{2)}}} is \sqrt[16]{2}

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

simplify

2

Decimal Notation

1.04427 \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:

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

Apply exponent rule:

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

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

\frac{1}{4} \cdot \frac{1}{4} = \frac{1}{16}

= 2^{\frac{1}{16}}

(3.87 \times 1 0^{- 5}) (5.96 \times 1 0^{- 9})

(a^{2} b c^{2}) (b^{2} c^{3}) (9 a)

- e^{- x} (x e^{- x})

8.56 \cdot 314.15 \cdot 1 0^{- 4}

What is sqrt(\sqrt{\sqrt{\sqrt{2)}}} ?
The solution to sqrt(\sqrt{\sqrt{\sqrt{2)}}} is \sqrt[16]{2}