## Solmyr 2 years ago Simplify: 5 sqrt 3 (2 sqrt 3 + 6 sqrt 19) 30 + 30 sqrt 57 90 + 30 sqrt 57 10 sqrt 3 + 30 sqrt 19 10 sqrt 3 + 30 sqrt 57

1. phi

same idea: distribute then combine sqrt's

2. Solmyr

im not sure how i would but it in distubutive property

3. Solmyr

put

4. Solmyr

5 srqt 3 (2 sqrt3 sqrt 3 + 6 sqrt 3 sqrt 19)??

5. phi

in letters: A * (B+C) = A*B + A*C take the "stuff" in front (in this case 3 sqrt3 ) and multiply it times each thing inside

6. phi

5 sqrt 3 (2 sqrt 3 + 6 sqrt 19) you have two terms inside the parens: 2 sqrt3 and 6 sqrt19 you multiply each term by 5 sqrt3 for the first term just write it like this 5*sqrt3 * 2 * sqrt3 ( I put in * to show the multiplication, but in algebra you normally don't show the multiplication sign, and just know it is there.) however, put the numbers first (when you multiply you can switch the order) 5*2 * sqrt3 * sqrt3 you know what 5*2 is , right ? do you know what sqrt3 * sqrt3 is ? and do the same thing for the 2nd term: 6 sqrt19

7. Solmyr

ok so 10 sqrt 6 and 5 * sqrt 3 * 6 * sqrt 19 giving me 5 * 6 and sqrt 3 * sqrt 19 then giving me 30 sqrt 57 Answer = 10 sqrt 6 + 30 sqrt 57

8. phi

giving me 5 * 6 and sqrt 3 * sqrt 19 then giving me 30 sqrt 57 that part is correct. do the first part again 5*2 * sqrt3 * sqrt3

9. Solmyr

5*2 = 10 sqrt 3 * sqrt 3 = sqrt 9 10 sqrt 9

10. phi

yes. but what is the square root of 9 ?

11. Solmyr

3

12. phi

yes so 10*sqrt(9) is 10*3 or 30

13. Solmyr

ok

14. Solmyr

so right now im looking at D for my answer

15. phi

what is the first term? (5*2 * sqrt3 * sqrt3) + (5 * sqrt 3 * 6 * sqrt 19)

16. Solmyr

the first term is 10 sqrt 9 simplified its 10 sqrt 3

17. Solmyr

next term is 30 sqrt 57

18. phi

the first term is 10 sqrt 9 simplified its 10 sqrt 3 <-- no. sqrt(9) is 3 square root of 9 is 3 because 3*3=9

19. Solmyr

ok

20. phi

so if you see sqrt(3*3) you know that is 3

21. Solmyr

ok

22. phi

so, the answer for this question is 10 sqrt 9 simplified its 10 *3 =30 for the first term.

23. Solmyr

ok

24. phi

can you get the answer ?

25. Solmyr

A

26. phi

yes, also I noticed a typo in my rules: sqrt(x) * sqrt(x) = x is the rule or sqrt( x*x) = x or sqrt(x^2) = x <-- (it is x, not 2 like I had) those are 3 different ways of saying the same thing. try to remember this rule.

27. Solmyr

ok thanks i'll post the last question if ur ready

28. phi

ok