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

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

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

simplify

2 + 3 \cdot 2 - 3

1

Solution steps

2 + 3 2 - 3

Apply radical rule:

a b = a \cdot b

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

= (2 + 3) (2 - 3)

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

= 1

Apply rule

1 = 1

= 1

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