## anonymous 5 years ago Help with rationalizing denominators equation is 1 over the square root 96 not sure what to do

1. anonymous

$1 FRACTION \sqrt{96}$

2. anonymous

$1/\sqrt{96} \times \sqrt{96}/\sqrt{96} = \sqrt{96}/9$

3. anonymous

$1/\sqrt{96}$$\sqrt{96}/(\sqrt{96}*\sqrt{96})$$\sqrt{96}/96$

4. anonymous

I understand I have to write the smallest number of a perfect square, but unsure of how to water that down. haha

5. anonymous

1 is the numerator. 96 is the denominator

6. anonymous

96|2 48|2 24|2 12|2 06|2 03|3 01|- $\sqrt{2^{5}*3}=4\sqrt{2*3}=4\sqrt{?}$

7. anonymous

2?

8. anonymous

$4\sqrt{6}/96 = \sqrt{6}/$

9. anonymous

$\sqrt{6}/24$

10. anonymous

would you mind explaining it?

11. anonymous

?

12. anonymous

in english haha

13. anonymous

to simplify a sqrt, you devide the number by primary numbers: 2,3,5,7,11,13,... until you get 1. The amount of primary is the amount of times you are multiplying it so as i did: 96|2 96/2 = 48 48|2 48/2 = 24 24|2 24/2 = 12 12|2 12/2 = 06 06|2 06/2 = 03 03|3 i can't devide 3 by 2 to get a non-decimal number so, i devide by the next primary which is 3 -> 03/3 = 1 01|- I have five 2's and one 3 therefore, 2^5*3 = 96

14. anonymous

$2^{5}*3^{1} = 2^{2}*2^{2}*2^{1}*3^{1} = 96$

15. anonymous

I somewhat get it a bit better.

16. anonymous

Times both the numerator and denomiator by $\sqrt{96}$ to get $1*\sqrt{96}/\sqrt{96}*\sqrt{96}$ Then the denominator becomes 96 and the numerator becomes $\sqrt{96}$ You then can simplify the numerator; $\sqrt{96} = \sqrt{16*64} =4\sqrt{6}$ As now both the numerator and denominator are divisible by 4 we can divide them both to make $\sqrt{6}/24$

17. anonymous

what should the answer look like?

18. anonymous

ah, I got it. I am just hazy on the whole find 1 thing that you mentioned earlier. how did you determine 16 and 64 for the square roots of 96??

19. anonymous

The answer is the smallest surd you can get ; $\sqrt{6}$ over the smallest integer you can get; 24 which equates to $\sqrt{6}/24$ ^^^ that's your answer..

20. anonymous

got that. so I have 10 over square root of 45 first step, mult 45 by 45

21. anonymous

OH DEAR>> I meant 16*6 not *64.. my computer is very slow so i can't see my errors in typing

22. anonymous

so is it that 6 is the smallest square root, and 16 is because it goes into 96 6 times--leaving a relation between 6 and 16?

23. anonymous

yeah :)

24. anonymous

ohhhkay cool. thanks dude!

25. anonymous

what if it has a factored numerator?such as $\sqrt{6}/\sqrt{28}$