gabriel wrote:
I am not sure about what you have done over here. Could you please explain in a bit more detail. Why did you add the powers ??.
We can't add the powers in this case - we can only do so for multiplication.
2^2 + 2^3 does NOT equal 2^5
2^2 * 2^3 DOES equal 2^5
The very first explanation details one of the best way to approach this question. Let's quickly review the principles behind it:
If n is a positive number, then the nth root of ANY number greater than 1 will always be greater than 1.
This rule follows from the fact that if you multiply two positive fractions, the product is smaller than either fraction. If you multiply 1 by 1, the product stays the same. If you multiply two numbers greater than 1, you get a product greater than either number.
So, the only way to build to a bigger product is to multiply two numbers greater than 1.
For this question, we want our product to be 4.
4 can be expressed as (# bigger than 1 * # bigger than 1). Therefore, 4^(1/2) is bigger than 1.
4 can be expressed as (# bigger than 1 * # bigger than 1 * # bigger than 1). Therefore, 4^(1/3) is bigger than 1.
4 can be expressed as (# bigger than 1 * # bigger than 1 * # bigger than 1 * # bigger than 1). Therefore, 4^(1/4) is bigger than 1.
We happen to know that 4^(1/2) = 2
So, our sum will be:
2 + (# bigger than 1) + (# bigger than 1)
When we add those up, we get a number bigger than 4: choose (e).
