# How do you simplify (3+sqrt 5)(3-sqrt 5) ?

Oct 16, 2015

$\left(3 + \sqrt{5}\right) \left(3 - \sqrt{5}\right) = 4$

#### Explanation:

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

This is an example of the difference of squares, $\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$, where $a = 3 \mathmr{and} b = \sqrt{5}$.

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

$9 - \sqrt{{5}^{2}}$

Apply the square root rule $\sqrt{{x}^{2}} = x$.

$9 - 5 = 4$