What is sqrt(\sqrt{\sqrt{\sqrt{5 32/16)}}} ?

The solution to sqrt(\sqrt{\sqrt{\sqrt{5 32/16)}}} is \sqrt[16]{7}

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simplify sqrt(\sqrt{\sqrt{\sqrt{5 32/16)}}}

simplify

5 \frac{32}{16}

Decimal Notation

1.12932 \dots

Solution steps

5 \frac{32}{16}

Convert mixed numbers to improper fractions:

5 \frac{32}{16} = \frac{112}{16}

= \frac{112}{16}

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:

= ((\frac{112}{16})^{\frac{1}{4}})^{\frac{1}{4}}

Apply exponent rule:

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

= (\frac{112}{16})^{\frac{1}{4} \cdot \frac{1}{4}}

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

= (\frac{112}{16})^{\frac{1}{16}}

Divide the numbers:

\frac{112}{16} = 7

x^{2} (a - x)^{2} (12 x^{2} - 12 a x + 2 a^{2})

33 \cdot 14.40279 \cdot e^{- 0.2 \cdot 14.40279}

(5 n^{7} m^{9}) \cdot (7 n^{2} m^{5})

e^{- 0.0602700000000 \dots \cdot 24} \cdot 50

3.02 \cdot 1 0^{- 1}

What is sqrt(\sqrt{\sqrt{\sqrt{5 32/16)}}} ?
The solution to sqrt(\sqrt{\sqrt{\sqrt{5 32/16)}}} is \sqrt[16]{7}