# How do you simplify 2(sqrt3)-4(sqrt2)+6(sqrt3)+8(sqrt2)?

May 29, 2017

See a solution below:

#### Explanation:

First, group like terms. In this problem the like terms are the radicals:

$2 \left(\sqrt{3}\right) + 6 \left(\sqrt{3}\right) - 4 \left(\sqrt{2}\right) + 8 \left(\sqrt{2}\right)$

Next, factor the common terms:

$\left(2 + 6\right) \left(\sqrt{3}\right) + \left(- 4 + 8\right) \left(\sqrt{2}\right)$

$8 \left(\sqrt{3}\right) + 4 \left(\sqrt{2}\right)$

Now, factor out the common term outside the radical:

$\left(4 \times 2\right) \left(\sqrt{3}\right) + 4 \left(\sqrt{2}\right)$

$4 \left(2 \left(\sqrt{3}\right) + \left(\sqrt{2}\right)\right)$

$4 \left(2 \sqrt{3} + \sqrt{2}\right)$

May 29, 2017

color(green)(4(sqrt2+2sqrt3)

#### Explanation:

$2 \left(\sqrt{3}\right) - 4 \left(\sqrt{2}\right) + 6 \left(\sqrt{3}\right) + 8 \left(\sqrt{2}\right)$

$\therefore = 2 \sqrt{3} + 6 \sqrt{3} - 4 \sqrt{2} + 8 \sqrt{2}$

$\therefore = 8 \sqrt{3} + 4 \sqrt{2}$

:.=color(green)(4(sqrt2+2sqrt3)

check:

:.color(green)(2(sqrt3)-4(sqrt2)+6(sqrt3)+8(sqrt2)=19.51326071

:.color(green)(4(sqrt2+2sqrt3)=19.51326071