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# Calculate square root in Java with Math sqrt

This is an example of how to calculate the square root in Java, using the `sqrt(double a)` method of Math Class. The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions. Calculating the square root of a number implies that you should:

• Use the `sqrt(double a)` method of Math Class. The method gets a double parameter and returns the correctly rounded positive square root of the number.

## 1. What is Square root in Java

When a number multiplies itself, the product is the square number. The number is the square root. We get perfect square roots for a perfect square number. The √ sign represents a square root. If x^2 is a square number, then x is the square root of it.

For Example, 1^2 = 1, therefore square root of 1 is 1. 2^2 = 4, therefore square root of 4 is 2. Similarly, 9^2 = 81, therefore square root of 81 is 9 and so on. One interesting to know about square root is that when 9 square, it gives 81 and when −9 squares it also gives 81. So we can say 9 and -9 both are the square root of 81.

## 2. Properties of Square Root

• A perfect square root exists for a perfect square number only.
• The square root of an even perfect square is even.
• An odd perfect square will have an odd square root.
• A perfect square cannot be negative and hence the square root of a negative number is not defined.
• Numbers ending with (having unit’s digit) 1, 4, 5, 6, or 9 will have a square root.
• If the unit digit of a number is 2, 3, 7, or 8 then a perfect square root is not possible.
• If a number ends with an odd number of zeros, then it cannot have a square root. A square root is only possible for even number of zeros.
• Two square roots can be multiplied. √5, when multiplied by √2, gives √10 as a result.
• Two same square roots are multiplied to give a non-square root number. When √25 is multiplied by √25 we get 25 as a result.

## 3. Java Math.sqrt()

The class `java.lang.Math` contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions. Math.sqrt() is a static method and is part of `java.lang.Math` class. This method calculates and returns the square root of a given number. Below is the declaration of `Math.sqrt()` method-

```public static double sqrt(double a)
```

## 4. Example

Let’s take an example to understand better how the Math.sqrt() method works in java-

```package com.javacodegeeks.examples.math.sqrt;

public class SquareRootDemo {
public static void main(String[] args) {

//Square root of negative numbers
System.out.println("Result of Math.sqrt(-4): " + Math.sqrt(-4));
System.out.println("Result of Math.sqrt(-1): " + Math.sqrt(-1));

//Square root of positive | negative zero
System.out.println("Result of Math.sqrt(0): " + Math.sqrt(0));
System.out.println("Result of Math.sqrt(-0): " + Math.sqrt(-0));

//Square root of positive numbers
System.out.println("Result of Math.sqrt(1): " + Math.sqrt(1));
System.out.println("Result of Math.sqrt(4): " + Math.sqrt(4));

//Square root of non-perfect square  numbers
System.out.println("Result of Math.sqrt(14): " + Math.sqrt(14));
System.out.println("Result of Math.sqrt(-14): " + Math.sqrt(-14));

//Square root of positive | negative Infinity
System.out.println("Result Positive Infinity: " + Math.sqrt(1.0 / 0));
System.out.println("Result negative Infinity: " + Math.sqrt(-(1.0 / 0)));

}
}

```

In the above example, We have taken all kind of values negative, zero, positive, perfect square and non-perfect square. Let’s have a look over the output to and see how does Math.sqrt() behaves with these numbers-

```Result of Math.sqrt(-4): NaN
Result of Math.sqrt(-1): NaN
Result of Math.sqrt(0): 0.0
Result of Math.sqrt(-0): 0.0
Result of Math.sqrt(1): 1.0
Result of Math.sqrt(4): 2.0
Result of Math.sqrt(14): 3.7416573867739413
Result of Math.sqrt(-14): NaN
Result Positive Infinity: Infinity
Result negative Infinity: NaN
```

By seeing the output of the program, we can conclude below points about Math.sqrt() method-

• If the argument is NaN or less than zero, then the result is NaN.
• If the argument is positive, then the result is positive.
• If the argument is positive zero or negative zero, then the result is the same as the argument.
• Otherwise, the result is the double value closest to the true mathematical square root of the argument value.

## 5. Conclusion

The square root is a common math operation which is required to implement other business logic. For Example, calculating diagonal of a right-angle triangle, implementing Pythagorean theorem, calculating trigonometric functions and etc.

This was an example of how to calculate the square root in Java, using the `sqrt(double a)` method of `Java.lang.Math` Class. Here is the source code of the examples used in this article.

You can download the full source code of this example here: Calculate square root in Java with Math sqrt

Last updated on Sept. 10, 2019  (No Ratings Yet)
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