Find the exact value of the radical expression in simplest form.

Question

anonymous · Answer

$$\sqrt{144}-\sqrt{40}-\sqrt{10}$$

goformit100 · Answer

do you know the Theory of Roots ?

anonymous · Answer

no i tried to do it an got $$3\sqrt{10}$$ @goformit100

anonymous · Answer

but i wasnt sure if its right

e.mccormick · Answer

Well, lets see  $\sqrt{144}-\sqrt{40}-\sqrt{10}\implies 12-4\sqrt{10}-\sqrt{10}$  I simplified first to see what could be added and subtracted.  So that will not just be a radical when done.

e.mccormick · Answer

Oops.  And that is $\sqrt{144}-\sqrt{40}-\sqrt{10}\implies 12-2\sqrt{10}-\sqrt{10}$  I made a mistake there.

anonymous · Answer

$$12-\sqrt{10}?$$

e.mccormick · Answer

Closer!  But the $-2\sqrt{10}$ is negative, so when you subtract another...

anonymous · Answer

$$12-3\sqrt{10}?$$

e.mccormick · Answer

Yes!  There it is.

anonymous · Answer

yay!!!! thnx lol

e.mccormick · Answer

I think you should be getting these soon.  You have had a few of them, and each one is a little different.  But hopefully you will soon understand the way radicals work.

anonymous · Answer

yea i hope so
i post the questions and tell them my answer to see if its right

e.mccormick · Answer

Which is a great way to do it.  It lets you get things checked out and corrected within minutes.  That helps.  

If you want the psychology of why it helps, it is called expert learning systems vs procedural learning.

anonymous · Answer

yea