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- Brent@GMATPrepNow
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√4If 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 = 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
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Brent
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- Jeff@TargetTestPrep
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We are given that M = √4 + ^3√4 + ^4√4. We need to determine the approximate value of M.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
Since √4 = 2, we need to determine the value of 2 + ^3√4 + ^4√4
Let's determine the approximate value of ^3√4. To find this value, we need to find the perfect cube roots just below and just above the cube root of 4.
^3√1 < ^3√4 < ^3√8
1 < ^3√4 < 2
Let's next determine the approximate value of ^4√4. To determine this value, we need to find the perfect fourth roots just below and just above the fourth root of 4.
^4√1 < ^4√4 < ^4√16
1 < ^4√4 < 2
Since both ^3√4 and ^4√4 are greater than 1, √4 + ^3√4 + ^4√4 > 2 + 1 + 1 = 4.
Answer: E
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√4 = 2
fourth root of 4 = 4^(1/4) = (2^2)^(1/4) = √2
So we've got 2 + √2 + (some number between 2 and √2), which means our sum is
2 + √2 + √2 < our sum < 2 + √2 + 2
The lesser of these (2 + √2 + √2) is ≈ 2 + 1.4 + 1.4, so our sum is greater than 4.
fourth root of 4 = 4^(1/4) = (2^2)^(1/4) = √2
So we've got 2 + √2 + (some number between 2 and √2), which means our sum is
2 + √2 + √2 < our sum < 2 + √2 + 2
The lesser of these (2 + √2 + √2) is ≈ 2 + 1.4 + 1.4, so our sum is greater than 4.