Subtracting radical expressions:

3^108-2^18-3^48 = ?

(I am using the ^ for the square root symbol since my computer doesn't have one)

Question

Subtracting radical expressions:

3^108-2^18-3^48 = ?

(I am using the ^ for the square root symbol since my computer doesn't have one)

jhannybean · Answer

Hmm. could you perhaps draw out your question using the drawing tool below? :)

jhannybean · Answer

I'll take a stab at it. $$3\sqrt{108}-2\sqrt{18}-3\sqrt{48}$$

Is that your question?/

anonymous · Answer

Yes sorry I didn't know where the drawing tool is lol

anonymous · Answer

Where is the drawing tool anyhow so I know for next time? Lol

jhannybean · Answer

You have your text book from which you are typing, and then 3 buttons below that: "equation" , "draw" and "attach"

anonymous · Answer

Oh gotcha thank you.

jhannybean · Answer

So you have got:$$3\sqrt{108}-2\sqrt{18}-3\sqrt{48}$$108, 18, and 48 all have a common multiple of 6, so first tell me:

6 x what = 108?

6 x what =18? 

6 x what = 48?

anonymous · Answer

6x18=108

6x3=18

6x8=48

jhannybean · Answer

Alright

anonymous · Answer

Ok but none of these seem to be a perfect square

jhannybean · Answer

6 x what = 18?

2 x what = 6?

2 x what = 8?

2 x what = 6?

anonymous · Answer

Sorry my teacher isn't very good at explaining :(

anonymous · Answer

6x3=18
2x3=6
2x4=8
2x3=6

jhannybean · Answer

We have to break it down by prime factorization. That is what we are doing now :)

anonymous · Answer

Oh ok this seems much better thank you for taking the time to do this with me :)

jhannybean · Answer

Sorry my post was deleted -.- OS is glitching out for me.

anonymous · Answer

No problem it happens lol

jhannybean · Answer

$$3\sqrt{108}-2\sqrt{18}-3\sqrt{48}$$$$3\sqrt{ 18 \cdot 6} -2\sqrt{6 \cdot 3} -3\sqrt{8 \cdot 6}$$$$3\sqrt{6\cdot\color{red}{ 3\cdot 3}}-2\sqrt{2\cdot \color{red}{3 \cdot 3}} - 3\sqrt{\color{red}{2 \cdot 2\cdot 2 \cdot 2}\cdot 3}$$ Now you see all the highlighted pairs? For every 2 of these, 1 comes out of the square root.

jhannybean · Answer

When it's pulled out of the square root, it gets multiplied to the number in front of the square root. $$3 \cdot 3\sqrt{6} - 2 \cdot 3\sqrt{2} - 3\cdot 2 \cdot 2\sqrt{3}$$ Now to get your answer you just simplify the numbers outside the parenthesis and you're done :)

anonymous · Answer

Awesome thank you so much! You're great :)

jhannybean · Answer

No problem. Good luck!

anonymous · Answer

Thanks :)