amitcpotnis wrote:
msali1983 wrote:
9^1/2 = 3
9^ 1/4= 1.732
Let 9^1/3 will have min value as 1.732 ( assumption) , no need for exact value
together 9^1/3 and 9^1/4 is more than 3 ( Considering min value)
so 9^1/2 - ( 9^1/3 +9^1/4) = value will always be less than zero.
But then what if you dont know the value of 9^1/3 and 9^1/4. I dont think that you can rely on this approach
Here is how i solved it:
Square root, cube root, fourth root are increasing function. for eg x^(1/2) greater the value of X greater is the value of square root, cube root, fourth root.
Lets use this info in this question.
square root of 9 is 3
Cube root of 8 is 2. 9 is greater than 8 so the cube root of 9 will be greater than 2 at-least.
Fourth root of 1 is 1. 9 is greater than 1. so the fourth root of 9 will be greater than 1.
Now lets combine the above three information.
You have 3 - (something greater than 2) - (something greater than 1)
hence the answer will be less than 0.
hope the explanation helped.
Please give kudos if you like the explanation.