# How do you simplify 2sqrt5(3+sqrt2)?

Apr 13, 2015

The Distributive Property of Multiplication tells us that color(blue)(a*(b + c ) = a*b + a* c

color(red)(2sqrt5(3+sqrt2)

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

$= 6 \sqrt{5} + 2 \left(\sqrt{5} \cdot \sqrt{2}\right)$

$= 6 \sqrt{5} + 2 \left(\sqrt{5 \cdot 2}\right)$ (Because color(blue)(sqrta*sqrtb = sqrt(a*b)

 color(green)(= 6sqrt5+2sqrt(10)