Simple one but do not get answer

[kuemura]

What is the value of M, M= sq root of 4 + cube root of 4 + quad root of 4?
Answer is: Greater than 4. Why?

My solution was:
sq root of 4 => 2
cube root of 4 => sq root of 2 => 1.4
quad root of 4 => sq root of 1.4 => 0.125

Total Sum: 2+1.4+0.125 = 3.525

[12rk34]

Originally Posted by kuemura

What is the value of M, M= sq root of 4 + cube root of 4 + quad root of 4?
Answer is: Greater than 4. Why?

My solution was:
sq root of 4 => 2
cube root of 4 => sq root of 2 => 1.4 [4^(1/3) = 2^(2/3)]
quad root of 4 => sq root of 1.4 => 0.125

Total Sum: 2+1.4+0.125 = 3.525

The expression in blue color is wrong.
Solution :
4^(1/2) + 4^(1/3) + 4^(1/4)
= 2 + 4^(1/3) + 2^(1/2)
> 4 , since 4^(1/3) > 1 and 2^(1/2) > 1

[kuemura]

12rk34, Thank you.

How can you know that 4 to the power of (1/3) is > 1? Any tricks? Or just out of memorization?

[eravi11]

Originally Posted by kuemura

12rk34, Thank you.

How can you know that 4 to the power of (1/3) is > 1? Any tricks? Or just out of memorization?

we know that 2^1/2 is greater than 1 and 4^1/3 = 2^2/3, so it will be greater than 1..

[kuemura]

Of course.... thx man.