anonymous 4 years ago what is the value of the expression sqrt(27)+sqrt(32)-sqrt(75)

1. anonymous

$\sqrt(27)+\sqrt(32)-\sqrt(75)$

2. anonymous

@zaynahf if your not busy can you help me out?

3. anonymous

Sure, i can! Do you know how to simplify radicals?

4. anonymous

not really

5. anonymous

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6. anonymous

To simplify radicals, you have to try to find a perfect square that fits perfectly into the number. So for the first one: $\sqrt{27}$ the biggest perfect square that can fit into it is 9. So, the inside would simplify to be: $\sqrt{9 \times 3} = 3\sqrt{3}$

7. anonymous

so i can get $\sqrt16X2 = 4\sqrt2 ?$

8. anonymous

Yeah! Now try the third one

9. anonymous

$\sqrt75 = \sqrt5X15 = 5\sqrt5?$

10. anonymous

No, since neither 15 nor 5 are perfect squares. Here are the perfect squares: 1,4,9,16,25,36,49,64,81,100....

11. anonymous

so $aaaannnnnd`im lost$

12. anonymous

lol i'll guide you through

13. anonymous

ok

14. anonymous

Ok since you want to get the biggest one that goes into there, start from the top of the list. Try seeing if 100 goes into 75 (obviously not), so just start from the smallest number after 75. 64,36,25,16,4,1. When you find the one that goes into 72, let me know.

15. anonymous

64

16. anonymous

64 goes into 75 evenly?

17. anonymous

oh no 25

18. anonymous

Good! Now what times 25 is 75?

19. anonymous

3

20. anonymous

So thats what goes under the radical: $\sqrt{75}= \sqrt{25 \times 3}= 5\sqrt{3}$ Right?

21. anonymous

ok what do i do now multiply them together?

22. anonymous

$3\sqrt{3}+4\sqrt{2}-5\sqrt{3}$ Is that what you have so far?

23. anonymous

yes

24. anonymous

There are only 2 with the same base radical, so you can only simplify those

25. anonymous

so i get $8\sqrt3+ 4\sqrt2$

26. anonymous

Remember, it's 3-5, not 3+5

27. anonymous

-2√3+4√2

28. anonymous

29. anonymous

Perfect

30. anonymous

Yes it is

31. anonymous

thnxs so much ^_^ now i can sleep ... eh maybe

32. anonymous

No problem! Let me know if you need other help