Let k represent some unknown positive non-integer less than 1. Where is each of the following located on a number line: - k, k-+2, k-3, √k, k²?

k-3, k-2, - k, k^2, sqrt (k), k+2

Step-by-step explanation:

k issome unknown positive non-integrer less than one. It means that k belongs to the interval (0,1).

The minimum value that k can take is one close to 0. If we take k=0.1, we have:

0.1-3 = - 2.9

0.1-2 = - 1.9

-k = - 0.1

For that reason, we know that k-3 < k-2 < - k. Those terms are located on the negative side of the number line.

Let's check the possitive side:

Given that k is a non-integer number less than 1, any number raised to the power of 2 is going to be less than the actual number. For that reason we locate k^2 next to zero.

Given that k is a non-integer number less than 1, the square rooth of any number is going to be greater than the actual number, but never greater than 1 ... For that reason sqrt (k) > k^2.

Last but not least, k+2 is the greatest number of all. Because in all cases, the less value it can take is 2.