Math.sqrt() in Java

Introduction

The Math.sqrt() in Java is present in java.lang.Math class and is used to calculate the square root of the given number. It returns the double value that is correctly rounded to the positive square root of a given double value. In the case of negative number input, it returns NaN(Not a Number) as the square root of a negative number is not real but an imaginary number. Since it is a static method, we can call it using its class name, such as Math.sqrt().

Method Declaration of Math.sqrt() Method in Java

Math.sqrt() method in Java is declared as follows:

It is a static method, i.e., it can be directly called using the Math class.

Syntax of Math.sqrt() in Java

To find the square root of a number we use the following syntax, pass the number num to sqrt() method. Also, num can be of the type int,float, or double. Lastly, we can store the result in another variable of Double type.

Parameters of Math.sqrt() in Java

Math.sqrt() method takes a single variable of double data type whose square root we are supposed to find.

Return Values of Math.sqrt() in Java

The Math.sqrt() method returns a double value that is the square root of the given value and a correctly rounded positive number. If the argument is NaN or a negative number, it returns NaN, i.e. Not a Number.

Examples of Math.sqrt() Method in Java

Let us see an example of finding the square root of the user's entered number.

Output:

Explanation:

We store the user-entered value into the num variable of double type, which is passed to the Math.sqrt() method. The Math.sqrt() method returns a double value stored in the squareRoot variable and printed.

Example: Special Cases

There are various special cases where we might expect a different value, such as the square root of infinity or a negative number.

Working of Math.sqrt() in Java

The square root of a number in Java is calculated using simple arithmetic operations such as addition, subtraction, multiplication, and division. Lastly, we get the desired answer with the help of loops. The mathematical formula used to find the square root precisely is given below.

Algorithm for Finding Square Root of a Number in Java

We first take two variables, num and half. num is left uninitialized, and half is initialized as value/2. We run a do-while loop; inside the do-while loop, we initialized num=half each time the loop runs and half = (num + value/num), where the value is a user-entered number. We run this loop until num is not equal to half. As this condition satisfies, half is the required square root of value.

Let us apply it to the Java code.

Output:

Square root using pow() method

There are other ways to find the square root of a number in Java except for the Math.sqrt() method. The first one we saw in the previous example was when we implemented our method that calculates the square root of a number. Another way is using the Math.pow() method, located in the same package as Math.sqrt(), i.e. java.lang.

The square root is nothing but a number to the power 1/2 (0.5 or half). We can pass 0.5 or 1/2 as the power to Math.pow() to get the square root of a number.

Let us see this example to compare Math.pow() and Math.sqrt() methods in Java.

Output:

Explanation:

In the example, we first ask for user input, which we later pass to both methods, Math.sqrt and Math.pow(), with power being 0.5. We can see that both methods return the same answer.

BigInteger sqrt() Method

BigInteger in Java is used where big integer calculations are required that are outside the range of integer or long data types. The java.math.BigInteger.sqrt() method returns a BigInteger that is the square root of the given BigInteger. It is just the same as floor(sqrt(num)), i.e., it returns a floor value unlike Math.sqrt(), which returns a double(numbers after decimal).

Syntax

The syntax of sqrt in Java of BigInteger is slightly different from that of Math.sqrt(). It takes no parameter, can only be called using objects of the BigInteger class, and returns the floor value of the square root of the respective BigInteger.

The below example illustrates the sqrt() method of the BigInteger class.

Output:

Explanation:

• The num variable is of the BigInteger type, which has 19 digits. The value of the num variable cannot be stored in an Integer or Long type variable.
• num.sqrt() returns a BigInteger that is the square root of num and is stored in squareRoot.
• Again, the square root of the given number is big enough that it cannot be stored in int data type.