# How do you simplify sqrt(1+x) * sqrt(1-x)?

Jul 17, 2018

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

#### Explanation:

Apply rule: $\sqrt{a} . \sqrt{b}$ = $\sqrt{a b}$

$\sqrt{1 + x} . \sqrt{1 - x}$

$\sqrt{\left(1 + x\right) . \left(1 - x\right)}$

We know that:
$\left(a + b\right) . \left(a - b\right)$ = ${a}^{2} - {b}^{2}$

So we get:

$\sqrt{\left(1 + x\right) . \left(1 - x\right)}$

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

Hope this helps!