What is sqrt(\sqrt[3]{4\sqrt[5]{16)}} ?

The solution to sqrt(\sqrt[3]{4\sqrt[5]{16)}} is \sqrt[30]{16}\sqrt[3]{2}

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simplify sqrt(\sqrt[3]{4\sqrt[5]{16)}}

simplify

34516

301632

Decimal

1.38191 \dots

Solution steps

34516

Apply radical rule:

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

= ((4516)^{\frac{1}{3}})^{\frac{1}{2}}

Apply exponent rule:

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

= (4516)^{\frac{1}{3} \cdot \frac{1}{2}}

\frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6}

= (4516)^{\frac{1}{6}}

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

= 64516

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= 646516

64 = 32

= 326516

6516 : 3016

= 323016

e^{- 10000}

3 (x - 1)^{2}

(x^{5} - 6 x^{3} - 8 x) (3 a^{2} x^{2})

(\frac{1}{2})^{- 2} ln (\frac{1}{2})

(4 x) (5 x^{2})

What is sqrt(\sqrt[3]{4\sqrt[5]{16)}} ?
The solution to sqrt(\sqrt[3]{4\sqrt[5]{16)}} is \sqrt[30]{16}\sqrt[3]{2}