I get confused only at the very end of this problem...I got the answer from the book:

(*= radical sign)

= 5 *3 - 2 *3

=(5 - 2) *3

= 3 *3

My question is: where does the other *3 go? Why is there only one *3 in the final answer?

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- May 5th 2008, 06:15 PMendlesst0mAdding and Subtracting Radicals with Different Radicands
I get confused only at the very end of this problem...I got the answer from the book:

(*= radical sign)

= 5 *3 - 2 *3

=(5 - 2) *3

**= 3 *3**

My question is: where does the other *3 go? Why is there only one *3 in the final answer? - May 5th 2008, 09:50 PMo_O
$\displaystyle 5\sqrt{3} - 2\sqrt{3} = 3\sqrt{3}$

Imagine $\displaystyle a = \sqrt{3}$: $\displaystyle 5a - 2a = 3a$ - May 5th 2008, 10:03 PMReckoner
The answer is: it's still there! You start off with two square roots of three being subtracted from five square roots of three. You are then left with three square roots of three, because 5 of something minus 3 of something is 2 of that something.

There may only be one*radical*in the final answer, but it is being multiplied by three, which is the same as adding it to itself twice.