How do you simplify 7[sqrt3] - 4[sqrt12]?

May 25, 2017

See a solution process below:

Explanation:

First, use this rule of radical multiplication to rewrite the expression:

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

$7 \left[\sqrt{3}\right] - 4 \left[\sqrt{12}\right] \implies$

$7 \left[\sqrt{3}\right] - 4 \left[\sqrt{4 \cdot 3}\right] \implies$

7[sqrt(3)] - 4[(sqrt(4) * sqrt(3)] =>

$7 \left[\sqrt{3}\right] - 4 \left[2 \cdot \sqrt{3}\right] \implies$

$7 \left[\sqrt{3}\right] - 8 \left[\sqrt{3}\right]$

Now, factor a $\sqrt{3}$ out of each term and combine like terms:

$7 \left[\sqrt{3}\right] - 8 \left[\sqrt{3}\right] \implies$

$\left(7 - 8\right) \left[\sqrt{3}\right] \implies$

$- 1 \sqrt{3} \implies$

$- \sqrt{3}$