Question

HELP PLZ: Simplify 2 times square root 12 minus 2 square root 9 plus square root of 112.

Answer 1

I got the last one btw

Answer 2

\(\Large 4\sqrt{24}-4\sqrt{8}+\sqrt{98}\)

Answer 3

yes @StudyGurl14

Answer 4

okay, so do you know how to simplify radicals?

Answer 5

kind of but for this one i forgot.

Answer 6

okay, let's start with 8. Try seperating it into its factors

Answer 7

4 and 2?

Answer 8

yep. keep going further. break down the 4

Answer 9

so break the 4 to 2 and 2

Answer 10

yep, so 8 = 2*2*2
Now, watch the magic:
\(\Large\sqrt{8}=\sqrt{2\times2\times2}=\sqrt{2^2\times2}=2\sqrt{2}\)

Answer 11

do you see how that worked?

Answer 12

yeah !

Answer 13

that actually did help a lot thanks!

Answer 14

actually, I just realized when didn't even have to break down the 4, because I'm sure you already know \(\sqrt{4}=2\)

Answer 15

yes

Answer 16

Yep, and since we had \(\Large-4\sqrt{8}\)...\(\Large-4(2\sqrt{2}=-8\sqrt{2}\)
Now, do you think you could do the same with \(\Large 4\sqrt{24}\)?

Answer 17

yes, so do I simplify inside the radical first? or the 4.

Answer 18

@StudyGurl14

Answer 19

inside the radical

Answer 20

@StudyGurl14 so i would get 6 and 4

Answer 21

@StudyGurl14

Answer 22

yep, so you'd get \(\Large 4\sqrt{24}=4\sqrt{6\times4}=?\)

Answer 23

would I factor out the 6 or the 4

Answer 24

the 4, because it can easily be turned into 2

Answer 25

oh ok! so I would now have 8 on the outside of the radical correct?

Answer 26

yep! So, so far we have:\(\Large 8\sqrt{6}-8sqrt{2}+\sqrt{98}\)

Can you do the last one now?

Answer 27

how did u get the 98

Answer 28

that's part of the original equation, remember? We haven't simplified that one yet

Answer 29

oh yea

Answer 30

i can't think off the top of my head what goes into 98....

Answer 31

well...it's an even number right? so try dividing it by 2

Answer 32

tell me what you get

Answer 33

49!

Answer 34

right! and what's \(\sqrt{49}\)?

Answer 35

8 would be the factor!

Answer 36

wait no, 7 sorry

Answer 37

:) right. so can you finish simplifying that one?

Answer 38

well, i would have 7 on the outside of the radical and then 7 on the inside right? but then what?

Answer 39

no, almost \(\Large\sqrt{98}=\sqrt{49\times 2}=7\sqrt{2}\)

Answer 40

im a little confused on this last step, i really want to learn but just still a lil confused

Answer 41

What exactly are you confused about?

Answer 42

well, what to do exactly next or how to know what to do next

Answer 43

Oh, okay. So now we have \(\Large 8\sqrt{6}-8\sqrt{2}+7\sqrt{2}\) right?

Answer 44

yes

Answer 45

Okay, so notice how both the -8 and 7 have a sqrt 2?

Answer 46

yep!

Answer 47

You can combine them like normal numbers. What is -8 + 7?

Answer 48

-1!

Answer 49

yep, so you get \(\Large 8\sqrt{6}-\sqrt{2}\)

You're done

Answer 50

oh wow, ok so what happened to the 98 again?

Answer 51

Remember, 98 = 49 times 2, so...\(\Large\sqrt{98}=\sqrt{49\times 2}=\sqrt{49}\times\sqrt{2}=7\sqrt{2}\)

Answer 52

and could i please have your help on one more?? you were super helpful and i actually learned

Answer 53

Make sense?

Answer 54

yes, completely!

Answer 55

Great. :) and yes, I'll help you with another, but in a new thread, since this one is awfully long now

Answer 56

ok, thank you!