• Apr 10th 2012, 03:17 AM
drmattthew
I've looked through dozens and dozens of questions, and I can't find an example with this format where both numbers in both sides are under the radical sign, and no numbers to the left, please help. (sqrt 3+4)(sqrt 3-7) The answer is 25-3-sqrt3 how do I get there??
• Apr 10th 2012, 03:45 AM
emakarov
What happens when you multiply through using the pattern $\displaystyle (a+b)(c+d)=ac+ad+bc+bd$?
• Apr 10th 2012, 09:26 AM
Soroban
Hello, drmattthew!

Quote:

$\displaystyle \left(\sqrt{3} + 4\right)\left(\sqrt{3}-7\right)$

Multiply as usual ("FOIL") . . . and simplify carefully.

$\displaystyle \left(\sqrt{3}+4\right)\left(\sqrt{3}-7\right) \;=\;\big(\sqrt{3}\big)\big(\sqrt{3}\big) + \big(\sqrt{3}\big)\big(\text{-}7\big) + \big(4\big)\big(\sqrt{3}\big) + \big(4\big)\big(\text{-}7\big)$

n . . . . . . . . . . . . . $\displaystyle =\qquad\quad 3 \quad\;\;-\;\quad 7\sqrt{3} \quad+\quad 4\sqrt{3} \quad-\quad 28$

n . . . . . . . . . . . . . $\displaystyle =\qquad\qquad \text{-}25 \;\;-\;\; 3\sqrt{3}$