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A. less than 3 B. equal to 3 C. between 3 and 4 D. equal to 4 E. greater than 4

Hi, the most important point here is that any number >1, if put to any root(100th root or 200th root) will always have a value >1.. now lets see the equation..

M = √4 + ∛4 + ∜4... we know √4=2 and both ∛4 and ∜4 will be >1.. s0 M=2+ something>1 +something>1.. or M is > than 4.. Ans E
_________________

I was wondering why we are not considering the negative roots of 4 in this case. For instance, sq root of 4 would be 2 and -2...same for the 4th root... Any rule / trick that I might be missing here?

Look forward to the answer.

Cheers!

Welcome to GMAT Club. Below might help to clear your doubts.

1. GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.

2. Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, \(\sqrt{25}=+5\) and \(-\sqrt{25}=-5\). Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

can someone explain how to do this type of questions in less time. If M = (4)^.5 + (4)^.3 + (4)^.25 , then the value of M is 1)less than 3 2) equal to 3 3)between 3 and 4 4)equal to 4 5)greater than 4

here \sqrt{4}=2 1<4^(1/3)<2 1<4^(1/4)<2

hence the sum, S;

4<S

P.S.: GO FOR THE FIXED MINIMUM VALUE THE ANSWER WILL BECOME EASY.

Hope this helps...!!
_________________

Practice Practice and practice...!!

If my reply /analysis is helpful-->please press KUDOS If there's a loophole in my analysis--> suggest measures to make it airtight.

Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the [#permalink]

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21 Apr 2012, 12:14

I was wondering why we are not considering the negative roots of 4 in this case. For instance, sq root of 4 would be 2 and -2...same for the 4th root... Any rule / trick that I might be missing here?

I noted down this question, but I forgot the source and cannot retrieve the correct answer. Needless to say the question asked for the approximate value of the equation & whether it was between, or greater/smaller than a combination of numbers, i.e. +/- 3 & 3/4, 3 & 4 and so forth. The question is whether there is a shortcut for simplifying this or looking at it under a different perspective other than sheer number sense, Thanks and apologies for being vague.

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