1. Jravenv

2. anonymous

1. simplify square roots to simplify the expression more: $((\sqrt{25}*\sqrt{3a})+(\sqrt{4}*\sqrt{3a})-(\sqrt{9}*\sqrt{3a}))/3a$

3. KyanTheDoodle

Probably gonna get banned for saying this, but every time I read your question, I see "best answer retarded"

4. anonymous

2. Next solve the square roots: $((5*\sqrt{3a})+(2*\sqrt{3a})-(3*\sqrt{3a})/\sqrt{3a}$

5. anonymous

Note: first step denominator should be square root 3a 3. the numerator has like terms so: $(5+2-3)(\sqrt{3a})/(\sqrt{3a})\rightarrow 5+2-3\rightarrow 4$

6. UsukiDoll

as I mentioned plenty times before...there are different methods to solving the problem in Mathematics as long as it doesn't break the Math rules.

7. UsukiDoll

but.. @hughfuve your answer isn't in the choices given... so something is wrong.

8. UsukiDoll

because ... (I hope I still remember this right) when you're changing to exponent form $\sqrt{3a} \rightarrow (3a)^{\frac{1}{2}}$

9. UsukiDoll

you're distributing that 1/2 all over

10. UsukiDoll

Ok. I know what's going on.. we need a $\sqrt{3a}$ in the numerator so we can cancel out the $\sqrt{3a}$ denominator

11. UsukiDoll

so we need to split up 75, 27, and 12

12. UsukiDoll

$\frac{\sqrt{75a}+\sqrt{12a}-\sqrt{27a}}{\sqrt{3a}}$

13. UsukiDoll

ok this is going to work :) we want that denominator to leave but before we have that we need to split up 75, 12, and 27.. we need perfect square numbers

14. UsukiDoll

is @Jravenv here right now? I want to guide her through this process we need to know what perfect squares can we use so we can take the square root so what is 3 x ? = 75, 3 x ? = 12, and 3 x ? = 27? there are 3 perfect square numbers

15. UsukiDoll

another way is what's 75/3, 12/4 , and 27/3 ???

16. UsukiDoll

sorry 75/3, 12/3, and 27/3

17. Jravenv

114/3

18. UsukiDoll

this is separate what is 75/3 or 3 x ? = 75

19. UsukiDoll

we're not adding those three fractions.. we are using division for 75/3 =? 12/3 =? 27/3 = ?

20. Jravenv

25

21. UsukiDoll

yes! so what about 12/3 = ? and 27/3 = ?

22. Jravenv

4 and 8 and a 3rd

23. UsukiDoll

what is 12 divided by 3? what is 27 divided by 3?

24. Jravenv

4 and 9

25. UsukiDoll

$\frac{\sqrt{25 \cdot 3 a}+\sqrt{4 \cdot 3a}-\sqrt{9 \cdot 3 a}}{\sqrt{3a}}$

26. UsukiDoll

so all we need is the square root of 25, 4, and 9 what is the square root of 25? what is the square root of 4? what is the square root of 9?

27. Jravenv

5 2 and 3?

28. UsukiDoll

yes.

29. UsukiDoll

$\frac{5\sqrt{ 3 a}+2\sqrt{ 3a}-3\sqrt{ 3 a}}{\sqrt{3a}}$

30. UsukiDoll

now we noticed that there is a term in common and I want to factor it out because i want to get rid of the denominator.. so what can we pull out of the numerator?

31. UsukiDoll

each term in the numerator has it, so it's safe to factor out :)

32. UsukiDoll

I can't factor 5 2 and 3 out, but I can factor _____________?

33. Jravenv

3a

34. UsukiDoll

$\frac{\sqrt{ 3 a}(5+2-3)}{\sqrt{3a}}$ yes notice that now we can get rid of the square root ?

35. UsukiDoll

we're left with a very simple equation... using order of operations PEMDAS... well just AS...we just add and subtract.

36. Jravenv

So its 4

37. UsukiDoll

yes it's 4. 5+2-3 using order of operations..addition first 5+2 = 7 7-3 (subtraction) 7-3 = 4

38. anonymous

geeez I completely forgot how to do that.. you are quite the doll usuki.