We are asked about the kinetic energy of an object. The kinetic energy is given by the following formula:

Where:

Part a) If the velocity is multiplied by 3 we have:

Solving the square we get:

Factoring out the 4 we get:

Therefore, the kinetic energy is multiplied by 9.
Part b) If the kinetic energy is multiplied by 4 we have in the formula:

We can move the 4 next to the velocity:

Now, by properties of exponents, we can rewrite the formula as:

Therefore, the velocity is multiplied by 2.
Part c can be solved using the same procedure as in par b.