Question

Is the square root of a number always larger than the cube root of that number?

Answer 1

The square root of a number is mostly always larger.

For example,

√25 =5 and ∛25≈2.92 5>2.92

√5879≈76.67 and ∛≈18.05 76.67>18.05

It works for those examples, but what if we use smaller numbers?

√1=1 and ∛1=1 1=1

√0=0 and ∛0=0 0=0

So, the square root of a number is larger than the cube root of a number, except in some cases when they are equal to each other.

Answer 2

Yes, always except when that number is 0 or 1. Take the number 64 for example. The square root of that is 8. The cubes root of that is 4. This is sense 8^2=64. So to raise the exponent the base must be smaller. Therefore a square root of a number will always be larger than the cubed root of it. Of course expect when the number is 1 or 0 as it doesn’t matter if it’s cubed or square root. It will still be 1 or 0