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Root Addition
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fourteenstix
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Brent@GMATPrepNow
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The square root of 4 = 2
The cube root of 4
The cube root of 1 = 1
The cube root of 8 = 2
So, the cube root of 4 is between 1 and 2.
In other words, the cube root of 4 = 1.something
The fourth root of 4
The fourth root of 1 = 1
The fourth root of 16 = 2
So, the fourth root of 4 is between 1 and 2.
In other words, the fourth root of 4 = 1.something
TOTAL SUM = 2 + 1.something + 1.something
= more than 4
= E
Cheers,
Brent
The cube root of 4
The cube root of 1 = 1
The cube root of 8 = 2
So, the cube root of 4 is between 1 and 2.
In other words, the cube root of 4 = 1.something
The fourth root of 4
The fourth root of 1 = 1
The fourth root of 16 = 2
So, the fourth root of 4 is between 1 and 2.
In other words, the fourth root of 4 = 1.something
TOTAL SUM = 2 + 1.something + 1.something
= more than 4
= E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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theCodeToGMAT
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√4 = 2
(4)^1/3 = will surely be greater than (1)^1/3 .. so, 1+
(4)^1/4 = will surely be greater than (1)^1/4 .. So, 1+
M = 2 + (1+) + (1+) = 4+
Answer [spoiler]{E}[/spoiler]
(4)^1/3 = will surely be greater than (1)^1/3 .. so, 1+
(4)^1/4 = will surely be greater than (1)^1/4 .. So, 1+
M = 2 + (1+) + (1+) = 4+
Answer [spoiler]{E}[/spoiler]
R A H U L
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Hi fourteenstix,
Brent's answer gives the clearest math explanation, but both explanations will get you to the correct answer. One of the ways to KNOW that you don't have to do an exact calculation is by the wording of the answer choices. In this case, since each is a "range" of values, the question itself is clue-ing you in that you don't need to do a ton of math to get the correct answer. In other questions, the word "approximate" is a clue to "round off" or estimate your math. Be on the lookout for these clues and you'll find it easier to get around the initial "shock" of what you're looking at and get to the correct answer.
GMAT assassins aren't born, they're made,
Rich
Brent's answer gives the clearest math explanation, but both explanations will get you to the correct answer. One of the ways to KNOW that you don't have to do an exact calculation is by the wording of the answer choices. In this case, since each is a "range" of values, the question itself is clue-ing you in that you don't need to do a ton of math to get the correct answer. In other questions, the word "approximate" is a clue to "round off" or estimate your math. Be on the lookout for these clues and you'll find it easier to get around the initial "shock" of what you're looking at and get to the correct answer.
GMAT assassins aren't born, they're made,
Rich
