# Square root and nth root in Octave

In this lesson I will explain how to calculate the square root and the nth root in Octave with a practical example.

## The square root

The square root of a number can be calculated using the built-in function **sqrt()**

**sqrt(n)**

The parameter n is the radicand of the root.

$$ \sqrt{n} $$

I'll give you some practical examples.

**Example 1**

Calculate the square root of 9

$$ \sqrt{9} $$

Type **sqrt(9)** on the command line

>> sqrt(9)

The output result is the number 3

ans = 3

**Example 2**

Alternatively, you can also calculate the square root using powers, indicating 1/2 as the exponent

$$ 9^{\frac{1}{2}} $$

In this case you have to type **9^(1/2)** on the Octave command line.

>> 9^(1/2)

ans = 3

The result is always the same

## The nth root

To calculate the nth root of a number you have to use the function **nthroot()**

**nthroot(n,i)**

This function has two parameters.

The first parameter (n) is the radicand, the second parameter (i) is the index of the radical.

$$ \sqrt[i]{n} $$

I'll give you some practical examples.

**Example 1**

Calculate the cube root or third root of 8

$$ \sqrt[3]{8} $$

Type **nthroot(8,3)** on the command line

>> nthroot(8,3)

The result is number 2

ans = 2

because

$$ 2^3 = 2 \cdot 2 \cdot 2 = 8 $$

**Example 2**

Calculate the fourth root of 81.

$$ \sqrt[4]{81} $$

Type **nthroot(81,4)** on the command line

>> nthroot(81,4)

The result is number 3

ans = 3

because

$$ 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81 $$

**Example 3
**

Alternatively, you can also calculate the fourth root using a power with exponent 1/4

$$ 81^{\frac{1}{4}} $$

In this case you have to write **81^(1/4)** on the Octave command line

>> 81^(1/4)

ans = 3

The result is the same.

So, you can calculate any nth root using Octave.