What is \sqrt[8]{(2-sqrt(7))^4} ?

The solution to \sqrt[8]{(2-sqrt(7))^4} is isqrt(\sqrt{7)-2}

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simplify \sqrt[8]{(2-sqrt(7))^4}

simplify

i 7 - 2

Solution steps

Apply radical rule:

= ((2 - 7)^{4})^{\frac{1}{8}}

Apply exponent rule:

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

= (2 - 7)^{4 \cdot \frac{1}{8}}

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

= (2 - 7)^{\frac{1}{2}}

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

= 2 - 7

Apply imaginary number rule:

- a = i a

= i 7 - 2

(3 x + 1)^{2} (- x + 4)^{2}

0.000001

\frac{e ^{7}}{e ^{3}}

What is \sqrt[8]{(2-sqrt(7))^4} ?
The solution to \sqrt[8]{(2-sqrt(7))^4} is isqrt(\sqrt{7)-2}