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by Brent@GMATPrepNow » Fri Oct 10, 2014 1:07 pm
If M = √4 + ∛4 + ∜4, then the value of M is:

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4
√4
√4 = 2

∛4
∛1 = 1
∛8 = 2
So, ∛4 is BETWEEN 1 and 2.
In other words, ∛4 = 1.something

∜4
∜1 = 1
∜16 = 2
So, ∜4 is BETWEEN 1 and 2.
In other words, ∜4 = 1.something

So, √4 + ∛4 + ∜4 = 2 + 1.something + 1.something
= more than 4
= E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Fri Oct 10, 2014 1:48 pm
Hi kamalakarthi,

As Brent has pointed out in his explanation, you don't really need to know the exact values of all 3 terms to answer the question. Notice how the answer choices are essentially "ranges" of answers? This is a clue that you don't necessarily need to calculate the exact answer. As you continue to study, be sure to pay attention to how the answer choices are written/formatted - they might provide a big clue as to how you can proceed through the prompt in the most efficient way possible.

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by Matt@VeritasPrep » Sat Oct 11, 2014 10:21 am
Just to add to Brent's solution:

√4 = 2

∜4 = √2 ≈ 1.4

(You can prove this as follows. ∜4 = 4^¼ = (2²)^¼ = 2^½ = √2.)

Since √4 > ∛4 > ∜4, we know that 2 > ∛4 > ≈1.4.

So √4 + ∛4 + ∜4 ≈ 2 + 1.6 + 1.4 ≈ 5. (This is remarkably close to the actual number, which is 5.0016...)
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