# How do you simplify (sqrt5-sqrt3)(sqrt5+sqrt3)?

Nov 13, 2017

$2$

#### Explanation:

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

As this question $\left(\sqrt{5} - \sqrt{3}\right) \left(\sqrt{5} + \sqrt{3}\right)$ is in a form of $\left(a + b\right) \left(a - b\right)$, we can simplify it into ${a}^{2} - {b}^{2}$ by subing $\sqrt{5} = a \mathmr{and} \sqrt{3} = b$ as the folllowing:

$\left(\sqrt{5} - \sqrt{3}\right) \left(\sqrt{5} + \sqrt{3}\right)$

$= {\left(\sqrt{5}\right)}^{2} - {\left(\sqrt{3}\right)}^{2}$

$= 5 - 3 = 2$
Here is the answer. Hope it can help you :)