# How do you simplify (3+2sqrt5)^2?

Sep 9, 2016

$12 \sqrt{5} + 29$

#### Explanation:

The square of a binomial gives a trinomial.
Each term in the first bracket must multiply by each term in the second bracket.

$\left(3 + 2 \sqrt{5}\right) \left(3 + 2 \sqrt{5}\right)$

=$9 + 6 \sqrt{5} + 6 \sqrt{5} + 4 \times 5$

=$12 \sqrt{5} + 29$

Recall: $\sqrt{x} \times \sqrt{x} = \sqrt{{x}^{2}} = {\left(\sqrt{x}\right)}^{2} = x$