How do you simplify  (3+sqrt5)(1+sqrt5)?

Feb 11, 2017

$8 + 4 \sqrt{5}$

Explanation:

The simplest way to expand this is to multiply each term in the second set of brackets with each term in the first set of brackets and then simplify the product. Hence:

$\left(3 + \sqrt{5}\right) \left(1 + \sqrt{5}\right)$

$3 \left(1 + \sqrt{5}\right) + \sqrt{5} \left(1 + \sqrt{5}\right)$

$\left(3 \times 1\right) + \left(3 \times \sqrt{5}\right) + \left(\sqrt{5} \times 1\right) + \left(\sqrt{5} \times \sqrt{5}\right)$

$3 + 3 \sqrt{5} + 1 \sqrt{5} + 5$

Collect like terms.

$\left(3 + 5\right) + \left(3 \sqrt{5} + 1 \sqrt{5}\right)$

$8 + \left(3 + 1\right) \sqrt{5}$

$8 + 4 \sqrt{5}$