Question

Help with rationalizing denominators
equation is 1 over the square root 96
not sure what to do

Answer 1

\[1 FRACTION \sqrt{96}\]

Answer 2

\[1/\sqrt{96} \times \sqrt{96}/\sqrt{96} = \sqrt{96}/9\]

Answer 3

\[1/\sqrt{96}\]\[\sqrt{96}/(\sqrt{96}*\sqrt{96})\]\[\sqrt{96}/96\]

Answer 4

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

Answer 5

1 is the numerator. 96 is the denominator

Answer 6

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

Answer 7

2?

Answer 8

\[4\sqrt{6}/96 = \sqrt{6}/\]

Answer 9

\[\sqrt{6}/24 \]

Answer 10

would you mind explaining it?

Answer 11

?

Answer 12

in english haha

Answer 13

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

Answer 14

\[2^{5}*3^{1} = 2^{2}*2^{2}*2^{1}*3^{1} = 96\]

Answer 15

I somewhat get it a bit better.

Answer 16

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
\[\sqrt{6}/24\]

Answer 17

what should the answer look like?

Answer 18

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??

Answer 19

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..

Answer 20

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

Answer 21

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

Answer 22

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?

Answer 23

yeah :)

Answer 24

ohhhkay cool. thanks dude!

Answer 25

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