If M= 4^1/2 +4^1/3+4^1/4, then teh value of M is
Less than 3
Equal to 3
Between 3 and 4
equal to 4
greater than 4
E
Roots
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- ssmiles08
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This problem is all about estimating values.
lets break it down by each 4.
4^1/2 = 2
4^1/3 = ?
you know 1^1/3 = 1 and 8^1/3 = 2
the cube root of 4 is some where b/w 1 and 2. Prefferably, it is somewhere around the 1.5 mark b/c 4 is halfway b/w 1 and 8
so we can approximate value of 4^1/3 ~ 1.5
4^1/4 = ?
you know 1^1/4 = 1 and 16^1/4 = 2
the 4th root of 4 lies some where b/w 1 and 2 again. This time 4 is closer to 1 than it is to 16, so we can approximate the value of 4^1/3 as ~ 1.1 or 1.2
so we have (2 + 1.5 + 1.1) which is collectively greater than 4.
(E)
lets break it down by each 4.
4^1/2 = 2
4^1/3 = ?
you know 1^1/3 = 1 and 8^1/3 = 2
the cube root of 4 is some where b/w 1 and 2. Prefferably, it is somewhere around the 1.5 mark b/c 4 is halfway b/w 1 and 8
so we can approximate value of 4^1/3 ~ 1.5
4^1/4 = ?
you know 1^1/4 = 1 and 16^1/4 = 2
the 4th root of 4 lies some where b/w 1 and 2 again. This time 4 is closer to 1 than it is to 16, so we can approximate the value of 4^1/3 as ~ 1.1 or 1.2
so we have (2 + 1.5 + 1.1) which is collectively greater than 4.
(E)