Problem Solving

Please help with this..

Tests the following concept: if the base is greater than 1, any root, not matter how high, CANNOT "drag" it below 1. 1 is the "border point" between "fractions" and "numbers greater than 1", and that border cannot be crossed by increase roots.

with this in mind, let's see what we have here:
sqrt(4) = 2 - that's easy.
cube root (4) is a number greater than 1.
If you're having trouble seeing this, think about what a cube root means: it is a number that, when cubed, will equal 4. Could that number be a fraction? If we take 9/10 and cube it, we get a smaller fraction, not 4. For the number to havea chance to reach 4 when cubed, it has to be greater than 1.
fourth root (4) is also a number greater than 1 - same as cube root (4).

Thus, the sum of the three terms must be greater than 2+1+1=4.

It also helps if you rewrite fourth root of 4 as follows: rewrite 4 as 2^2, and convert the fourth root to a power of "quarter", so 4th root of 4 becomes (2^2)^1/4, or 2^1/2, or sqrt(2).
If you remember than sqrt (2) is approximately 1.4 (a ballpark that helps in many GMAT questions, esp. Geometry), then you sum is already 2+1.4 + a number in the middle, which must be smaller than 2 but greater than 1.4 = definitely greater than 4.

M=4^.5+4^1/3+4^1/4

M=2+ I guessed is around 1.5 and 1.2

So must add up above 4

Geva@MasterGMAT wrote:Tests the following concept: if the base is greater than 1, any root, not matter how high, CANNOT "drag" it below 1. 1 is the "border point" between "fractions" and "numbers greater than 1", and that border cannot be crossed by increase roots.

Very Important Concept,

If i can remember that, I am sure that will help me sometime in future..........