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

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

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

simplify

a - a^{2} - 1 a + a^{2} - 1

1

Solution steps

a - a^{2} - 1 a + a^{2} - 1

Apply radical rule:

a b = a \cdot b

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

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

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

= 1

Apply rule

1 = 1

= 1

\frac{1}{3} \times \frac{3}{3}

(2.8 \times 1 0^{- 4}) (16)^{1.08}

e^{- 0.02 \cdot 0.02617}

- 2 e^{- \frac{1}{2}}

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