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## Homework Statement

Hey guys/gals I have need a clarification on one particular pre-algebra problem dealing with multiplying radicals. I thought I knew the steps to solve it (properties of radicals and distribution property, etc) but I am having trouble with this particular problem.

(8√6 +√5)(√6+9√5)

## The Attempt at a Solution

Okay so I used used FOIL as if I was multiplying two binomials together so

(8√6 *√6) + (8√6 * 9√5) and (√5 *√6) + (√5 *9√5)

1) 8√6 *√6= 48 because (√n*√n= n)

2) I proceeded to use the Distribution property so 8√6 * 9√5= 72√30

3) Repeating step two with inner term: √5*√6=√30

4) Lastly inner term x outer term:√5 *√5 = √25

Okay so after using the Distribution property the new equation looks like this:

48+72√30+√30+9 √25

5) now I take take the square root of √25 which is 5 and multiply it by 9:

....9√25 becomes 45

now the equation reads:

48+72√30+√30+45

6) Now I add like terms and this is the point where I am missing a step or have messed up in some way in the above steps. After combining like terms I get:

93+73√30

the correct answer is 73√30+93

I thought addition was commutative so I didn't think that the order mattered but why when I combine 48 & 45 the sum ends up on the end of the equation and why does the order matter if addition is commutative? I got this question wrong because of the order but I've looked at this problem for a while now and I don't understand why the correct answer is in the order it is in and why it matters.

Also I'm sorry this was a long post and elementary problem but I just don't understand any clues to lead me in the right direction would be much appreciated. Thanks in advance for reading this or replying to it. And I hope this is in the right format, apologies if it isnt.