 # Simplify Square Root Calculator

   

A step by step online calculator to simplify the square root of positive integers is presented.

## Simplifying the Square Root of a Positive Integer

How to simplify the square root of a positive integer is shown here as an example which is also the default example of the calculator when this page download the first time.
Example
Simplify $\sqrt {2420}$
Step 1: Use
prime factorization to write $2420$ as a product of powers of prime numbers.
Successive divisions of n by the prime numbers 2, 3, 5, 7, 11, 13, ...gives
$\dfrac{2420}{\color{red}2} = 1210$
$\dfrac{1210}{\color{red}2} = 605$
$\dfrac{605}{\color{red}5} = 121$
$\dfrac{121}{\color{red}{11}} = 11$
$\dfrac{11}{\color{red}{11}} = 1$
Hence the prime factorization of $2420$ is
$2430 = 2 \times 2 \times 5 \times 11 \times 11$
Hence $2420 = 2^2 \times 5 \times 11^2$
Step 2: Take the square root of both sides
$\sqrt{2420} = \sqrt{2^2 \times 5 \times 11^2}$
Step 3: Use the product rule of radicals $\sqrt {x \times y} = \sqrt x \times \sqrt y$ to rewrite the above as
$\sqrt{2420} = (\sqrt{2^2}) \times (\sqrt {5}) \times (\sqrt {11^2})$
Step 4: Simplify the above using the rule: $\sqrt{x^m} = x^{\dfrac{m}{2}}$
$\sqrt{2420} = 2^1 \times (\sqrt {5}) \times 11^1$
Step 5: Simplify by mutliplying the coefficients outside the radicals toghether and the radicands together.
$\sqrt{2420} = 22 \times \sqrt {5}$

## Use the calculator to Simplify Square Root

1 - Enter a positive integer n and press "Simplify The Square Root of n". The steps in simplifying the square root are listed below.

 Enter Positive Integer n = 2420
Solution