What is sqrt((x^2-1)^2-1) ?

The solution to sqrt((x^2-1)^2-1) is xsqrt(x^2-2)

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simplify sqrt((x^2-1)^2-1)

simplify

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

x x^{2} - 2

Solution steps

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

Expand

(x^{2} - 1)^{2} - 1 : x^{4} - 2 x^{2}

= x^{4} - 2 x^{2}

Factor out common term

x^{2} : x^{2} (x^{2} - 2)

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

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

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

= x^{2} x^{2} - 2

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

x^{2} = x

= x x^{2} - 2

- 3 80 a^{7}

8 x - 3 - 5 x + 2 x + 12

x^{5} y + y^{3}

(a s + 1) (b s + 1)

\frac{1}{5} + \frac{4}{3}