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# sqrt, sqrtl and sqrtf in C++

There are various functions available in the C++ Library to calculate the square root of a number. Most prominently, sqrt is used that is defined in <cmath> header file. It takes double as an argument. The <cmath> header defines two more inbuilt functions for calculating the square root of a number (apart from sqrt) which has an argument of type float and long double.

Following are the functions used for calculating square root in C++ :

1. sqrt (double)
2. sqrtf (float)
3. sqrtl (long double)

The above functions have been discussed in detail below:

## 1. sqrt()

The sqrt() function returns the square root of a number of type double.

### Syntax

`double sqrt(double arg);`

## C++

 `// CPP code to illustrate the use of sqrt function``#include ``#include ``#include ``using` `namespace` `std;` `// Driver Code``int` `main()``{``    ``double` `val1 = 225.0;``    ``double` `val2 = 300.0;` `    ``// Calculate and print the square root of val1``    ``cout << fixed << setprecision(12) << ``sqrt``(val1) << endl;``    ``// Calculate and print the square root of val2``    ``cout << fixed << setprecision(12) << ``sqrt``(val2) << endl;` `    ``return` `(0);``}`

Output

```15.000000000000
17.320508075689
```

### Complexity Analysis

• Time Complexity: O(√n)
• Auxiliary Space: O(1)

### Errors and Exceptions Associated with sqrt() Function

1. It is mandatory to give the argument otherwise, it will give an error no matching function for call to ‘sqrt()’ as shown below.

## C++

 `// CPP Program to demonstrate errors in double sqrt()``#include ``#include ``using` `namespace` `std;` `// Driver Code``int` `main()``{``    ``double` `answer;` `    ``// no value is passed as parameter``    ``answer = ``sqrt``();``    ``cout << ``"Square root of "` `<< a << ``" is "` `<< answer``         ``<< endl;` `    ``return` `0;``}`

Output

```prog.cpp:9:19: error: no matching function for call to ‘sqrt()’

2. If we pass a negative value in the argument domain error occurs and the output will be the Square root of -a, which is -nan.

## CPP

 `// CPP Program to demonstrate errors in double sqrt()``#include ``#include ``using` `namespace` `std;` `// Driver Code``int` `main()``{``    ``double` `a = -2, answer;``    ``// Calculate the square root of a``    ``answer = ``sqrt``(a);``    ``cout << ``"Square root of "` `<< a << ``" is "` `<< answer``         ``<< endl;` `    ``return` `0;``}`

Output

```Square root of -2 is -nan
```

## 2. sqrtf()

The sqrtf() function returns the square root of a number of type float.

### Syntax

`float sqrtf(float arg)`

## C++

 `// CPP code to illustrate the use of sqrtf function``#include ``#include ``#include ` `using` `namespace` `std;` `int` `main()``{``    ``float` `val1 = 225.0;``    ``float` `val2 = 300.0;``    ``// Calculate and print the square root of val1``    ``cout << fixed << setprecision(12) << sqrtf(val1)``         ``<< endl;``    ``// Calculate and print the square root of val2``    ``cout << fixed << setprecision(12) << sqrtf(val2)``         ``<< endl;` `    ``return` `(0);``}`

Output

```15.000000000000
17.320508956909
```

### Complexity Analysis

• Time Complexity: O(√n)
• Auxiliary Space: O(1)

## 3. sqrtl()

The sqrtl() function returns the square root of a number of type long double with more precision.

### Syntax

`long double sqrtl(long double arg)`

## C++

 `// CPP program to illustrate the use of sqrtl function``#include ``#include ``#include ``using` `namespace` `std;``int` `main()``{``    ``long` `long` `int` `var1 = 1000000000000000000;``    ``long` `long` `int` `var2 = 999999999999999999;``    ``// Calculate and print the square root of val1``    ``cout << fixed << setprecision(12) << sqrtl(var1)``         ``<< endl;``    ``// Calculate and print the square root of val2``    ``cout << fixed << setprecision(12) << sqrtl(var2)``         ``<< endl;` `    ``return` `0;``}`

Output

```1000000000.000000000000
999999999.999999999476
```

### Complexity Analysis

• Time Complexity: O(√n)
• Auxiliary Space: O(1)

When working with integers of the order 1018, calculating its square root with sqrt function may give an incorrect answer due to precision errors as default functions in programming language work with floats/doubles. But sqrtl function will always give an accurate answer.

Following is an illustration given below shows the exact difference when working with long integers with sqrt and sqrtl.

1) Using sqrt function

## C++

 `// CPP code to illustrate the incorrectness of sqrt``// function``#include ``#include ``#include ` `using` `namespace` `std;` `int` `main()``{``    ``long` `long` `int` `val1 = 1000000000000000000;``    ``long` `long` `int` `val2 = 999999999999999999;` `    ``// Calculate and print the square root of val1``    ``cout << fixed << setprecision(12) << ``sqrt``(val1) << endl;``    ``// Calculate and print the square root of val2``    ``cout << fixed << setprecision(12) << ``sqrt``(val2) << endl;` `    ``return` `(0);``}`

Output

```1000000000.000000000000
1000000000.000000000000
```

2) Using sqrtl function

## C++

 `// CPP code to illustrate the correctness of sqrtl function``#include ``#include ``#include ` `using` `namespace` `std;` `int` `main()``{``    ``long` `long` `int` `val1 = 1000000000000000000;``    ``long` `long` `int` `val2 = 999999999999999999;` `    ``// Calculate and print the square root of val1``    ``cout << fixed << setprecision(12) << sqrtl(val1)``         ``<< endl;``    ``// Calculate and print the square root of val2``    ``cout << fixed << setprecision(12) << sqrtl(val2)``         ``<< endl;` `    ``return` `(0);``}`

Output

```1000000000.000000000000
999999999.999999999476
```