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# Powers

``````1public class Ex9 {
2  public static void main(String[] args) {
3    int alpha = 5;
4    double beta = Math.pow(5, 2);
5    System.out.println("5 to the power of 2 is " + beta);
6
7    int gamma = 5.5;
8    double delta = Math.pow(5.5, 2.2);
9    System.out.println("5.5 to the power of 2 is " + delta);
10
11    int epsilon = 10;
12    int zeta = (int) Math.pow(5, 2);
13    System.out.println("5 to the power of 2.2 is " + zeta);
14
15    int eta = 4;
16    double sqrt = Math.sqrt(4);
17    System.out.println("The square root of 4 is " + sqrt);
18
19    int theta = 5;
20    sqrt = Math.sqrt(5);
21    System.out.println("The square root of 5 is " + sqrt);
22  }
23}
``````

### Explanation

1. In this exercise, we introduce the functions `Math.pow()` and `Math.sqrt()`. `Math.pow()` puts the first argument to the power of the second argument. It takes a double for both its arguments, hence why we can do `Math.pow(5.5, 2.2)`. It's fine to put integers as its arguments, since integers can be implicitly cast to doubles. `Math.sqrt()` takes one double as an argument, and returns its square root. `Math.pow()` and `Math.sqrt()` return doubles as well.

2. If you want to store the values returned from `Math.pow()` and `Math.sqrt()` as integers, as in line 13, then you must explicitly cast it by putting `(int)` in front of the double you want to cast to an int. The reason that doubles aren't implicitly cast to integers is because doubles are more precise.

### Extension Programs

1. Use a for loop, to write a program that prints out all the numbers between 1 to 100, squared.

2. Use a for loop, to write a program that prints out 2 to the power of 1, 2 to the power of 2, all the way to 2 to the power of 16.

3. Given that momentum = mass * (velocity to the power of 2), write a program to calculate momentum given mass and velocity. You will need to store mass and velocity as variables, and calculate momentum from the variables.

4. Write a program to calculate BMI (Body Mass Index) using the formula: BMI = mass / (height to the power of 2). You will need to store mass and height as variables, and calculate BMI from the variables.