Simplify the expression???

Question

(3√5 + 2√10) (4√5 - 6√10)

The answer has to be in √ form

I know how to do it but I don't know how to answer it in √ form. Can I know the steps on how to answer it like that?

Answer 1

multiply it out

12√25  + 8√50 + 18√50 + 12√100

12*5 + 8√25*2 + 18√25*2 + 12 √ 25*4

60 + 40√2 + 90√2 + 120

200 + 130√2 ....is ur answer :)

  

Answer 2

(3√5+2√10)(4√5 - 6√10)

= (3√5 *4√5)-(3√5*6√10)+(2√10*4√5)-(2√10*6√10)

=60-18√50 + 8√50 - 120

= -10√50 - 60

= -10√25√2 -60

=(-10*5)√2 -60

= -50√2 -60

Answer 3

solve it like a FOIL problem. multiply together the Firsts, then the Outers, then the Inners, then the Lasts.

3root5 x 4root5 = 12 x 5 since 3 and 4 = 12, and root5 x itself is 5.

12 x 5 is 60. keep that off to the side. do the same with 3root5 and -6root10 (remember the negatives), then 2root10 and 4root5, and then 2root10 and -6root10. then add (or subtract) those together the best you can, and simplify them if you can.

for the ones that don't have the same roots, i'm not sure if you know how to do that but multiply the things in roots together, for example root10 and root5, to get root50, which you can simplify to 5root2. makes sure to multiply the 5 with you other stuff you get on the outside of the root for that stage of the problem. hope this made sense!

Answer 4

No matter what I do it never comes out in √ form.

Only one way will do it but I'm not sure if it's right.

(3√5 x -6√10) + (2√10x 4√5) =

-18√50 + 8√60 =

-10√50

Hope that helps!

Answer 5

Use FOIL, then combine the roots. For example:

sqrt(5)*sqrt(10) = sqrt(5*10) = sqrt(50) = 5sqrt(2)