What is sqrt(x+\sqrt{x^2-1)}sqrt(x-\sqrt{x^2-1)} ?

The solution to sqrt(x+\sqrt{x^2-1)}sqrt(x-\sqrt{x^2-1)} is 1

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simplify sqrt(x+\sqrt{x^2-1)}sqrt(x-\sqrt{x^2-1)}

simplify

x + x^{2} - 1 x - x^{2} - 1

1

Solution steps

x + x^{2} - 1 x - x^{2} - 1

Apply radical rule:

a b = a \cdot b

x + x^{2} - 1 x - x^{2} - 1 = (x + x^{2} - 1) (x - x^{2} - 1)

= (x + x^{2} - 1) (x - x^{2} - 1)

(x + x^{2} - 1) (x - x^{2} - 1) = 1

= 1

Apply rule

1 = 1

= 1

x^{m} y^{n} (2 (x^{3} - 1) y e^{y^{2}})

5.3 \cdot 1 0^{- 23}

0.022 \cdot 22.5 \cdot 1 0^{- 3} \cdot 156 0^{2}

3 (5)^{6} \cdot (e)^{- \frac{30}{8}}

\frac{e ^{5}}{e ^{2}}

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