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by divya23 » Thu Jun 09, 2011 7:57 am
if m = root 4 + cuberoot 4 + quadroot 4

find value of m

[spoiler]ans = greater than 4[/spoiler]
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by cans » Thu Jun 09, 2011 8:02 am
root 4 + cuberoot 4 + quadroot 4
root(4)=2
2>cuberoot 4 >1 (1^3=1 and 2^3=8)
2>quadroot 4>1 (1^4=1 and 2^4=16)
Thus 6>m>4
m is greater than 4
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by GMATGuruNY » Tue Jun 14, 2011 10:33 am
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Since the problem above asks only for an estimation, we can ballpark:

√4 = 2.
4^(1/3) > 1.
4^(1/4) = √2 ≈ 1.4.

So M > 4.4.

The correct answer is E.
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by Anurag@Gurome » Thu Feb 16, 2012 8:53 pm
divya23 wrote:if m = root 4 + cuberoot 4 + quadroot 4

find value of m

[spoiler]ans = greater than 4[/spoiler]
m = √4 + (4)^(1/3) + (4)^(1/4)
m = 2 + (4)^(1/4) + (4)^(1/3)
m = 2 + (2²)^(1/4) + (4)^(1/3)
m = 2 + √2 + (4)^(1/3)
m = 2 + 1.4 + (4)^(1/3)
m = 3.4 + (4)^(1/3)

To find (4)^(1/3), we know that (4)^(1/4) is 1.4 approx, so (4)^(1/3) should lie between 1.4 and 2

Therefore, [spoiler]m > 4.8[/spoiler] and hence m > 4
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