What is \sqrt[n]{2+sqrt(3)}*\sqrt[n]{2-sqrt(3)} ?

The solution to \sqrt[n]{2+sqrt(3)}*\sqrt[n]{2-sqrt(3)} is 1

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simplify \sqrt[n]{2+sqrt(3)}*\sqrt[n]{2-sqrt(3)}

simplify

1

Solution steps

Apply radical rule:

= ((2 + 3) (2 - 3))^{\frac{1}{n}}

(2 + 3) (2 - 3) = 1

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

Apply rule

1^{a} = 1

= 1

(5.2 \cdot 1 0^{15}) (6.5 \cdot 1 0^{- 8})

(3 e^{3 x}) (x e^{3 x})

(3 x^{2}) (7 x^{2})

What is \sqrt[n]{2+sqrt(3)}*\sqrt[n]{2-sqrt(3)} ?
The solution to \sqrt[n]{2+sqrt(3)}*\sqrt[n]{2-sqrt(3)} is 1