Melzy11 Posts: 7, Reputation: 1 New Member #1 Jun 8, 2007, 09:52 AM
How to check to see if an answer is correct
How do I go back to see if the problem is correct. If I did the problem correctly, which is 12x^1/4 =24 I would have come out with x=8. That is assuming I did it correctly. If it is correct, how do go back and check to make sure? I think that you plug in the 8 but where? :confused:
 bekah876 Posts: 445, Reputation: 38 Full Member #2 Jun 8, 2007, 10:39 AM
Plug 8 into x. 8 is the correct answer here. 12(8)^(1/4) =24
 ebaines Posts: 12,132, Reputation: 1307 Expert #3 Jun 8, 2007, 10:57 AM
Sorry, but the correct answer to this problem is 16, not 8: 12*(16^1/4) = 12*2 = 24. The answer of 8 would be correct if the problem had been 12x^1/3 = 24.

However, it is correct that the way to check your work is to shove the answer for x back into the original equation and see if it works out.
 galactus Posts: 2,271, Reputation: 282 Ultra Member #4 Jun 8, 2007, 01:06 PM

$12x^{\frac{1}{4}}=24$

$x^{\frac{1}{4}}=2$

$x=2^{4}=16$
 bekah876 Posts: 445, Reputation: 38 Full Member #5 Jun 8, 2007, 01:06 PM
I thought the problem was 12x^(1/4)=24. Which means you would multiply 12 * x before raising it to (1/4). I could be wrong. I tried to use my fancy TI-86 but the bateries are dead.

I hate that I got a negative remark for trying to help with a math problem.

Okay I see how to work the problem now. The correct answer is 16.
 ebaines Posts: 12,132, Reputation: 1307 Expert #6 Jun 8, 2007, 01:21 PM
Originally Posted by bekah876
I thought the problem was 12x^(1/4)=24. Which means you would multiply 12 * x before raising it to (1/4).
If that was the case, then the answer would be 27,648:

12 * 27,648 = 331,776

(331,776) ^ 1/4 = 24.

Remember that the correct order of operations is to do exponents before multiplication. Since the original post said 12x^(1/4), that means 12[x^(1/4)].

Perhaps there is some confusion here over what x^(1/4) means. Raising a number to a fraction like 1/n means you take the "nth" root of x. The answer is 16 because the 4th root of 16 is 2, and 12 times 2 is 24. The 4th root of 8 is an irrational number, approximately 1.682, and 2 times that is 3.3635.. not 24.
 ebaines Posts: 12,132, Reputation: 1307 Expert #7 Jun 8, 2007, 01:31 PM
Originally Posted by Melzy11
I tried it as 12x^1/3 = 24 and came up with 6. I am very confused now. Please someone help me :confused:
Melzy - I think I know your problem - it seems that you are treating the "^" symbol like multiplication. That would explain why you keep getting 8 for 12*x^(1/4)=24, and 6 for 12*x^(1/3)=24. You're solving this:

$
12 X (\frac 14) = 24
$

when you should be solving:
$
12 X ^ {\frac14} = 24
$

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