Simplify square root of 1-x^4

$\sqrt{1 - x^{4}}$

Write the expression using exponents.

Rewrite $1$ as $1^{2}$ .

$\sqrt{1^{2} - x^{4}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{1^{2} - {(x^{2})}^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x^{2}$ .

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

Simplify.

Rewrite $1$ as $1^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

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

Simplify square root of 1-x^4

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