# How do you simplify (sqrt2+sqrt7)(sqrt 2+sqrt 7)?

May 4, 2017

See a solution process below:

#### Explanation:

This is a special form of the quadratic factored:

${\left(a + b\right)}^{2} = \left(a + b\right) \left(a + b\right) = {a}^{2} + 2 a b + {b}^{2}$

Substituting $\sqrt{2}$ for $a$ and $\sqrt{7}$ for $b$ gives:

$\left(\sqrt{2} + \sqrt{7}\right) \left(\sqrt{2} + \sqrt{7}\right) = {\sqrt{2}}^{2} + 2 \sqrt{2} \sqrt{7} + {\sqrt{7}}^{2} =$

$2 + 2 \sqrt{2} \sqrt{7} + 7$

We can now use this rule for multiplying radicals to simplify the middle term:

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$

$2 + 2 \sqrt{2 \cdot 7} + 7 =$2 + 2sqrt(14) + 7 =#

$9 + 2 \sqrt{14}$