What is (sqrt(2-\sqrt[3]{5)})^4 ?

The solution to (sqrt(2-\sqrt[3]{5)})^4 is 4-4\sqrt[3]{5}+\sqrt[3]{5^2}

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simplify (sqrt(2-\sqrt[3]{5)})^4

simplify

Decimal Notation

0.08411 \dots

Solution steps

Rewrite

4

2 \cdot 2

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

Apply exponent rule:

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

2^{2} = 4

(n - 1) \cdot 2^{m} n^{m}

3.2 \cdot 1 0^{- 7}

3.2 \cdot 1 0^{- 8}

5 \cdot e^{- 2}

What is (sqrt(2-\sqrt[3]{5)})^4 ?
The solution to (sqrt(2-\sqrt[3]{5)})^4 is 4-4\sqrt[3]{5}+\sqrt[3]{5^2}