Multiplying Radicals: Solving Pre-Algebra Homework

[Illuvitar]

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.

 

[Ray Vickson]

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.

Your answer is OK: 93 + 73√30 = 73√30 + 93. Why would you think otherwise?

 

[Illuvitar]

Well because it was graded as wrong and I didn't get partial credit either. I thought I followed the correct procedure but I just don't understand what exactly I did wrong.

 

[Ray Vickson]

Well because it was graded as wrong and I didn't get partial credit either. I thought I followed the correct procedure but I just don't understand what exactly I did wrong.

Was this graded by a computer, or by a real person?

 

[Mark44]

If the "correct" answer was 73√30+93 and you wrote 93 + 73√30 and this was marked wrong, go see your instructor. As already mentioned, the two expressions represent exactly the same number.

 

[Illuvitar]

Was this graded by a computer, or by a real person?

By my instructor.

If the "correct" answer was 73√30+93 and you wrote 93 + 73√30 and this was marked wrong, go see your instructor. As already mentioned, the two expressions represent exactly the same number.

Okay. I'm sorry for the redundant thread, I just thought there was something I missed. I thought they were the same answer but was open to the idea that there was just something I didn't understand. Ill talk to my instructor. Thanks guys.