Question

Solve for m

Answer 1

\[\sqrt{m-7} = n+3 \]

Answer 2

To get rid of the square root, you need to square both sides. Do you know how to do that?

Answer 3

\[m^2-49 = n^2 + 9 ?\]

Answer 4

mmm....no.

\[\sqrt{m-7} = n+3\]Square both sides\[\sqrt{m-7}*\sqrt{m-7} = (n+3)(n+3)\]\[m-7 = n^2 + 3n + 3n + 9\]Can you solve that?

Answer 5

I think so ... \[m=n^2+6n+2?\]

Answer 6

Close. But not close enough :-) Try again? How did you move the 7?

Answer 7

ohhhhh haha sorry add POSITIVE 7 hahaha so, 16 at the end?

Answer 8

yes!

Answer 9

So do you understand how I squared both sides?

Answer 10

hahaha yep :) Thank you :) You are good at explaining the steps and making sure I understand them :) haha

Answer 11

I was squaring the individuals :3 haha

Answer 12

Excellent, you wouldn't believe how many people don't realize that doesn't work :-)

Answer 13

hahaha I was one of 'em :) haha thank you so much, again :)

Answer 14

and easy to demonstrate:

5^2 = 5*5 = 25

(2+3) = 5
(2+3)^2 = (2+3)(2+3) = 25 which doesn't equal 4 + 9!

Answer 15

sometimes trying out algebra expressions with actual numbers like that makes it easier to see why it does (or doesn't) work...

Answer 16

Yeah, I do that sometimes but I never thought to do it with this kind of question :) haha I am so happy I can finally understand this :)

Answer 17

Another happy customer :-)

Answer 18

Got another to do?

Answer 19

It is sort of like this, we are just learning about radicals in general but it's this one... https://media.glynlyon.com/g_alg01_2013/8/test15.gif

Answer 20

It's probably really simple but I just don't know where to start... :\

Answer 21

I mean it looks simple haha

Answer 22

\[\frac{x}{2}+1 = \sqrt{3}\]Is that it?

Answer 23

yep

Answer 24

Okay, you know how to do this, I'm sure. It's the radical sign that is making you not so sure...

What if you had\[\frac{x}{2}+1=3\]Would you know how to solve that for \(x\)?

Answer 25

subtract one and multiply by 2

Answer 26

Indeed. And that's just what you do here!

Answer 27

oh, really??

Answer 28

But you can't subtract the 1 from the 3 underneath the square root sign. Here's what happens:
\[\frac{x}{2} + 1 = \sqrt{3}\]Subtract 1 from both sides\[\frac{x}{2}+1-1 = \sqrt{3}-1\]\[\frac{x}{2} = \sqrt{3}-1\]Now what do you do next?

Answer 29

oh!!! is it \[2\sqrt{3}-2\]

Answer 30

It is!

Answer 31

See, I told you you already knew how to do it :-)

Answer 32

Hahahaha!!!! Yesssss!! lol thank you soooo much!!!

Answer 33

lol I've had a good bit of problems in this course that we are working on and I finally get it :D haha I get a little "excited" when I learn how to do a new thing haha

Answer 34

Thank you so much :)

Answer 35

You're welcome! Actually, reactions like that are why I do this :-)