## A community for students. Sign up today

Here's the question you clicked on:

## anonymous 4 years ago simplify the expression square root of 27 times square root of 2

• This Question is Closed
1. anonymous

$\sqrt{27}\times \sqrt{2}$

2. anonymous

3sqrt3 *sqrt2 = 3sqrt6

3. Hero

= sqrt{27*2} = sqrt{54} = sqrt{9*6} = sqrt{9} * sqrt{6} = 3 sqrt{6}

4. anonymous

how did you get 3 square roots of three

5. anonymous

27=9*3 sqrt(9*3)=3sqrt3

6. anonymous

ok ?

7. anonymous

so take the perfact square of 9 out of 27 so 9 times 3 =27 then the suare root of 9 is 3 so 3 suare roots of the 3 that cant be simplified right

8. anonymous

yes

9. Hero

If you use my approach, you wouldn't have to worry about running into 3 sqrt{3}

10. anonymous

ok ya i think Hero's way makes a little more sence. thanks though

11. anonymous

so 27 times 2 =54 than take the perfect square root of 9 out so 9 times 6= 54 then simplify so 3 square roots of 6 corect?

12. anonymous

so as another example $\sqrt{10} \times \sqrt{8}$ 10 times 8 is 80 then take 16 out so 16 times 5 = 80 then simplify to 4 square roots of 5 is that how it works?

13. Hero

yup

14. Hero

good job

15. anonymous

ok but what about $\sqrt{12} \times \sqrt{18}$ i have a fealing theres an extra step i don't know how to do

16. Hero

It's the same strategy...look for the highest square, then split it up into a square root of two numbers, one being a square.

17. Hero

If you multiply 12*18 you get 216. 216/6 = 36 so do sqrt{36*6}

18. anonymous

i got 18 times 12 is 216 then 9 times 24 so 3 is from the 9 and the 24 also can go to 4times 6 which is 2 square roots of 6 so would i add 3+ 2

19. anonymous

and make it 5square roots of 6

20. Hero

Basically, there are two strategies to finding the square. You either divide by multiples of two until you find a square, or you divide by squares until you get a non-decimal integer.

21. Hero

Basically, I did this: 216/2 no 216/4 no 216/6 yes Or you can find the nearest square and divide by that like so: 216/196 no 216/169 no ... 216/36 yes It depends on which number you're working with but either way works.

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy