simplify sqrt3 (sqrt6 - 2 sqrt3)?

Question

Please help?

Answer 1

First, a helpful thing for you to know is if you want to type √, just type "& radic;" but without the space after the &. I put it there so you could actually see the code.

Anyways, so you have:
√3 (√6 - 2√3)

Distribute that √3. You will get this:
√18 - 2√9.

You can simplify this. Think of it this way:
(√9 * √2) - 2√9

What is √9? 3. So wherever you see that, just pull out the 3:
(3 * √2) - 2 * 3

Now, combine like terms and write it normally:
3√2 - 6

If you wanted to, you could keep the 3 factored out and it would just look like this. This is probably what your teacher wants:
3(√2 - 2)

But yeah, that is your answer! You can't do anything else because you can't add or subtract things if they have different square roots with them! (In this case, 6 doesn't have one, so yeah, you can't substract it from 3√2 and still be able to write it as a radical.)

I hope this clears things up. Keep in mind that you won't always be able to simplify it all the way because of little obstacles like this.

Answer 2

sqrt3 (sqrt6 - 2 sqrt3)

Expand out...

sqrt (18) - 2 (3)
sqrt (18) - 6

sqrt 18 = sqrt 9 * sqrt 2 = 3sqrt(2)

3sqrt(2) - 6

Answer 3

You can multiply within the sqrts, since sqrt(a) x sqrt(b) = sqrt (ab). So.............
Expression= sqrt 18- 2 sqrt 9.
we see somthing sneaky, that sqrt 9 = 3. So that can be factored out of both terms......
Expression = 3 sqrt(2) -6
Factor out a 3 to get 3(sqrt(2) -2)

Answer 4

(1) Distribute: sqrt(3) * sqrt(6) - 2 * sqrt(3) * sqrt(3)

(2) Combine square roots through multiplication:
sqrt(18) - 2 * sqrt(9)

(3) Simplify:
3 sqrt(2) - 6

Good luck!

Answer 5

re write
sqrt 3 ( sqrt 2*sqrt 3-2sqrt3)
factor out sqrt 3
sqrt3*sqrt3 ( sqrt2-2)
3(sqrt2-2)

Answer 6

1. sqrt(3)[sqrt(6) - 2sqrt(3)]
2. [sqrt(3)] [sqrt(6)] - 2sqrt(3) [sqrt(3)]
3. sqrt(3x6) - 2sqrt(3x3)
4. sqrt(18) - 2sqrt(9)
5. sqrt(9x2) - 2sqrt(9)
6. [sqrt(9)] [sqrt(2)] - 2sqrt(9)
7. 3sqrt(2) - 2(3)
8. 3sqrt(2) - 6
9. 3 [sqrt(2) - 2 ]