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

The solution to sqrt(\sqrt{2\sqrt{2\sqrt{2)}}} is \sqrt[4]{2}\sqrt[4]{2^{3/4}}

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

simplify

222

Decimal Notation

1.35425 \dots

Solution steps

222

Apply radical rule:

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

= ((222)^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

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

= (222)^{\frac{1}{2} \cdot \frac{1}{2}}

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

= (222)^{\frac{1}{4}}

22 = 2^{\frac{3}{4}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

(\frac{1}{3} r^{7}) (4 r^{6})

e^{- x} \cdot ln (\frac{1}{x})

8.854 \cdot 1 0^{- 12} (\frac{0.00025}{0.006})

40 (1.661 \cdot 1 0^{- 27})

What is sqrt(\sqrt{2\sqrt{2\sqrt{2)}}} ?
The solution to sqrt(\sqrt{2\sqrt{2\sqrt{2)}}} is \sqrt[4]{2}\sqrt[4]{2^{3/4}}