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Comment on Eighth Powers
((a+b)^2)^4 = ((a-b)^2)^4
This is a simpler way because in both cases when you expand (a+b)^2 OR (a-b)^2 ; 2ab will be 0. Hence both quantities become (a^2 +b^2)^4.
But sir am unable to score.
Your score breakdowns don't
Your score breakdowns don't provide much information regarding what's needed to increase your scores.
The GRE is a test of your math and verbal skills AND it's a test of your test-taking skills. So, taking several practice tests is an important part of your prep. This will help you build your test-taking skills, and it will help you identify any remaining area(s) of weakness.
While analyzing your practice tests, there are four main types of weakness to watch out for:
1. specific Quant skills/concepts (e.g., algebra, geometry, etc.)
2. specific Verbal skills/concepts (e.g., vocabulary, 3-blank text completion questions, etc.)
3. test-taking skills (time management, endurance, anxiety etc.)
4. silly mistakes
For the first two weaknesses, the fix is pretty straightforward. Learn the concept/skill and find some practice questions to strengthen that weakness.
If your test-taking skills are holding you back, then you need to work on these. For example, we have a free video about test anxiety at http://www.greenlighttestprep.com/module/general-gre-info-and-strategies...
Finally, if silly mistakes are hurting your score, then it's important that you identify and categorize these mistakes so that, during tests, you can easily spot situations in which you're prone to making errors. I write about this and other strategies in the following article: http://www.greenlighttestprep.com/articles/avoiding-silly-misteaks-gre
if we square root 3 times
Then Quantity A and B would not be equal. Is there any error, if I use this procedure.
In this case, answer is D.
There's an inherent problem
There's an inherent problem with finding the roots of expressions that are already raised to a power. The reason for this is that EVEN powers will turn any value into a POSITIVE number.
For example, 3^4 = 81 AND (-3)^4 = 81
Likewise, 5^2 = 25 AND (-5)^2 = 25
Now if we find the square root of 5^2 (aka 25), we get 5.
Likewise, if we find the square root of (-5)^2 (aka 25), we also get 5 (not -5).
Many students make the mistake of concluding that √(k²) = k, but this is ONLY true if k is greater than or equal to zero. If k is negative, then √(k²) ≠ k.
For example, √[(-3)²] = √9 = 3 (not -3)
So, with your solution, we cannot say that √(a-b) = a-b, if it's the case that a-b has a NEGATIVE value.
I took the 8th root to get
A property of exponents is
A property of exponents is that a number raised to an EVEN power will yield a value that is greater than or equal to zero.
For example, (-2)^8 = 256 AND 2^8 = 256
More here: https://www.greenlighttestprep.com/module/gre-powers-and-roots/video/1023
So, if we know that x^8 = y^8, we can't conclude that x = y. It could be the case that x = -2 and y = 2.
what if we have (a+b)^5 and
on that case, are we allowed to take 5th root on both side?
Yes. If the exponent is odd,
Yes. If the exponent is odd, then we can do that.
So, if (a+b)^5 = (a-b)^5, then we can conclude that a + b = a - b
The question doesn't make
Rather than just stating the
Rather than just stating the correct answer is D (which is not true), try identifying specific values of a and b that PROVE the correct answer is D. You'll find that it's impossible to do.
Here's a quick example that contradicts your statements that we can simply take the 8th root of both quantities.
QUANTITY A: (-1)^8
QUANTITY B: 1^8
Here it's obvious that the two quantities are equal.
However, look what happens if we take the 8th root of both quantities, as you suggest.
QUANTITY A: -1
QUANTITY B: 1
By taking the 8th root of both quantities, we incorrectly come to the conclusion that Quantity B is greater.
Would it be too simplistic to
That theory will work, but
That theory will work, but only when one of the values is 0 (as in the question).
If neither value is 0, then we can't use that approach.
For example, if a = 2 and b = 1, then:
(a-b)^8 = (2-1)^8 = 1^8 = 1
(a+b)^8 = (2+1)^8 = 3^8 = 6561
We can't square root or
The issue with raising both
The issue with raising both quantities by some power (e.g., power of 1/8) is that the sign (positive or negative) of the base may not be preserved.
For example, we can't conclude that (x^8)^(1/8) = x
Here's what I mean: if x = -1, then (x^8)^(1/8) = 1 (not -1)
Does that help?
My mistake here was to think
-(b^8). Parenthesis are really important.This is the type of mistakes I make.
You're not alone. I often see
You're not alone. I often see students make that same mistake.
I took this approach: (a+b)^2
That's a solid approach.
That's a solid approach.
I would add that the same property holds true for (a-b)^8, in that (a-b)^2 gives a^2 + b^2 - 2ab, and since ab=0, we get a^2 + b^2.