If M = 4^(1/2) + 4^(1/3) + 4^(1/4), then the value of M is

[ginakim85]

If M = 4^(1/2) + 4^(1/3) + 4^(1/4), 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

Answer: E.

Sorry if this has already been posted, but nothing came up when I searched for it. Thanks!

[kamsmandal]

You can try below trick. You don't have to actually calculate, this can go in your mind...

4^(1/2) = 2
4^(1/4) approx = 1.4
so, 4^(1/3) will be between 2 and 1.4. Definitely more than 1.

If you add all the three sum is greater than 4.
Thats option E.

Regards,
Kamna

[adiagr]

If M = 4^(1/2) + 4^(1/3) + 4^(1/4), 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

Answer: E.

Sorry if this has already been posted, but nothing came up when I searched for it. Thanks!

4^(1/2) = 2
4^(1/4) = 2^0.5 = 1.1416

adding above two, we get: 3.1416, so A, B out.

Now 1^(1/3) is 1 and 8^(1/3) is 2

so 4^(1/3) will be between 1 & 2

(3.1416 + 1) < desired result < (3.416 + 2)

4.1416 < desired result < 5.416

C & D also out

E is the answer.

Aditya

[mschwrtz]

Aditya, do you carry that info around in your head?

I agree with kamsmandal that you should be able to estimate sqrt2 as 1.4.

All you need here though is 2 + more than 1 + more than 1=more than 4.

[debmalya.dutta]

M = 4^(1/2) + 4^(1/3) + 4^(1/4) = 2 + 2^2/3 + 2 ^ 1/2
we know that 1 ^3 =1 ..so 2^2/3 > 1.???(something greater than 0 after the decimal)
we know that 1 ^ 2 = 1
So 2^1/2 = 1. ????(something greater than 0 after the decimal)

Replacing this in the equation for M, we have
M= 2 + 1.??? + 1.????
M > 4 for sure

[RonPurewal]

try here:
if-m-square-root-4-cube-root-4-fourth-root-of-4-then-t567.html