Question

Simplifying Radical Expressions

Answer 1

can you give the prime factorization of 96???

Answer 2

What is the Prime Factorization?

Answer 3

I mean what does that mean...my bad lol

Answer 4

give me the the numbers that multiply to 96 ....

Answer 5

ok..that might take me a sec to figure out. hang on..

Answer 6

HINT: since 96 is even, it is divisible by 2....

Answer 7

so is it 48?

Answer 8

ok... so:

96 = 2 * 48

can you give me a factorization of 48 ????

Answer 9

HINT: 48 is also even....

Answer 10

24?

Answer 11

ok good... so:
96 = 2 * 2 * 24

can you factorize 24 ??

Answer 12

12?

Answer 13

ok... keep going until you cant factor anymore starting with the 12...

96 = 2 * 2 * 2 * 12

Answer 14

ok so next it would be 6, and then 3?

Answer 15

yes... tell me if this is correct:
96 = 2 * 2 * 2 * 2 * 2 * 3

Answer 16

yes that is correct

Answer 17

ok... so....

Answer 18

\(\huge \sqrt{96}=\sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3} \)

for every PAIR of 2's inside the radical, you can eliminate them both inside the radical and write it once OUTSIDe of the radical.....

how many PAIRS of 2's are inside the radical???

Answer 19

is there 3 pairs for two?

Answer 20

2

Answer 21

there are two pairs of 2 inside with a 2 and a 3 left over.. you agree?

Answer 22

yes.

Answer 23

ok... so the two pairs can be crossed out from the radicand and written outside of the radical sign:

Answer 24

\(\huge \sqrt{96}=\sqrt{\color {red}{2 \cdot 2 \cdot 2 \cdot 2 }\cdot 2 \cdot 3} \)
\(\huge \sqrt{96}=2 \cdot 2\sqrt{\color {red}{\cancel {2 \cdot 2} \cdot\cancel { 2 \cdot 2} }\cdot 2 \cdot 3} \)
\(\huge = 4\sqrt6 \)

Answer 25

so its \[\sqrt{96}=\sqrt[4]{6}\]

Answer 26

be careful.....
\(\huge 4\sqrt6 \) is DIFFERENT from \(\huge \sqrt[4]6 \)

Answer 27

ohh shoot..ok thanks...and also I was thinking is would be \[16\sqrt{6}\] since those two pairs of 2 multiply out to 16?

Answer 28

well... you didn't really need to do prime factorization to do this problem IF you realized that
96 = 16 * 6. then it would have been easier:
\(\huge \sqrt{96}=\sqrt{16\cdot6}=\sqrt{16} \cdot \sqrt{6}=4\sqrt6 \)

Answer 29

ohhh i see.

Answer 30

but the procedure we just went through works EVERYTIME...

Answer 31

really? so that is the asnwer to my problem?

Answer 32

that helped me out, I learned something there :P

Answer 33

the answer is posted twice....

Answer 34

ok. would you mind helping me with 3 more? they are a bit different from this one..

Answer 35

yeah... just post it as a new question....

Answer 36

ok. will do. thank you!!

Answer 37

yw...:)