## anonymous 5 years ago (3sqrt(7) -6sqrt(3)) (3sqrt(7) +9sqrt(3)) multiply to solve.

1. anonymous

I got -99+9sqrt(21)

2. anonymous

1.) 3sqrt(2) * [3 + sqrt(2)] Distribute for each term: 9sqrt(2) + 3sqrt(2)*sqrt(2) (Multiplying like roots cancels it out to the actual number, 2 in this case) 9sqrt(2) + 3*2 9sqrt(2) + 6 2.) 4 + sqrt(20)/2 Assuming that the 2 is being divided into ONLY the sqrt(20)... 4 + 2sqrt(5)/2 (The 2s cancel here because of division) 4 + sqrt(5) In the case that the 2 is being divided into BOTH the 4 and the sqrt(2)... [4 + 2sqrt(5)]/2 2 + sqrt(5) 3.) 12sqrt(18)/3sqrt(2) Again, simplify the roots as much as possible... 12*3sqrt(2)/3sqrt(2) (The 3sqrt(2) cancels because of division) 12 So, your answers are 1.) 9sqrt(2) + 6 2.) 4 + sqrt(5) (or 2 + sqrt(5), depending) 3.) 12

3. anonymous

Wow, great explanation!

4. anonymous

$(3\sqrt{7} -6\sqrt3) (3\sqrt7 +9\sqrt3) = 9*7 + 27\sqrt21 - 18\sqrt21 - 54*3 = 63 + 9\sqrt21 - 162 = -99 + 9\sqrt21$

5. anonymous

or that lol

6. anonymous

Thanks

7. anonymous