Can someone help me with simplifying radicals? I'll comment my question I'm stuck on.

Question

Can someone help me with simplifying radicals?  I'll comment my question I'm stuck on.

anonymous · Answer

This is what I've gotten so far: $$16\sqrt{343}=16\sqrt{49\times7}=16\sqrt{49}\times \sqrt{7}=272\sqrt{7}$$ I am not sure if it's right! If I'm wrong, can you go through it with me?

unklerhaukus · Answer

You've started off right, factoring the term under the sqrt
and breaking it up,
but i think you made a multiplication error,  [16×7≠272]
$$16\sqrt{343}=16\sqrt{49\times7}=16\sqrt{49}\times \sqrt{7}=16\times7\times\sqrt7=...\sqrt{7}$$

unklerhaukus · Answer

just check that multiplication step     16×7 = ...

anonymous · Answer

Oh, I got that.  So would the final answer be: $$112\sqrt{7}$$?

unklerhaukus · Answer

Yes!

anonymous · Answer

Okay, thank you for catching my mistake!  I thought I got all of the steps right, but I had a feeling I made a mistake! @UnkleRhaukus

unklerhaukus · Answer

mistakes are easy to make , i still make (simple) multiplication errors all the time

unklerhaukus · Answer

one method to check this sort of problem is with a calculator 

[16][×][√(343)] = 296.3241468392341
   [112]][×][√7] = 296.3241468392341

anonymous · Answer

Cool!  That's nice to know!