What is sqrt(\sqrt[8]{256)} ?

The solution to sqrt(\sqrt[8]{256)} is square root of 2

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simplify sqrt(\sqrt[8]{256)}

simplify

2

Decimal Notation

1.41421 \dots

Solution steps

Apply radical rule:

= (25 6^{\frac{1}{8}})^{\frac{1}{2}}

Apply exponent rule:

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

= 25 6^{\frac{1}{8} \cdot \frac{1}{2}}

\frac{1}{8} \cdot \frac{1}{2} = \frac{1}{16}

= 25 6^{\frac{1}{16}}

Factor the number:

256 = 2^{8}

Apply exponent rule:

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

= 2

[(2^{3})^{4}]^{2}

e^{- 274.67}

e^{2} \cdot x^{2}

8 (3) e^{- 3}

What is sqrt(\sqrt[8]{256)} ?
The solution to sqrt(\sqrt[8]{256)} is square root of 2