What is sqrt(\sqrt{\sqrt{\sqrt{5)}}} ?

The solution to sqrt(\sqrt{\sqrt{\sqrt{5)}}} is \sqrt[16]{5}

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simplify sqrt(\sqrt{\sqrt{\sqrt{5)}}}

simplify

5

Decimal Notation

1.10582 \dots

Solution steps

5

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:

= (5^{\frac{1}{4}})^{\frac{1}{4}}

Apply exponent rule:

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

= 5^{\frac{1}{4} \cdot \frac{1}{4}}

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

= 5^{\frac{1}{16}}

500 \cdot 60 \cdot 60 \cdot 24 \cdot 30 \cdot \frac{1}{3.6 \cdot 1 0 ^{6}} \cdot 0.1762

e^{4 (t - 3)} cos (5) (t - 3) u (t - 3)

φ^{- 1} (0.9)

e^{- s i n (x)} e^{s i n (x)}

2000 (1 + \frac{0.24}{4})^{- 2}

What is sqrt(\sqrt{\sqrt{\sqrt{5)}}} ?
The solution to sqrt(\sqrt{\sqrt{\sqrt{5)}}} is \sqrt[16]{5}