A step by step online calculator to simplify the square root of positive integers is presented.
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.
\( \sqrt{2420} = 22 \times \sqrt {5} \)
1 - Enter a positive integer n and press "Simplify The Square Root of n". The steps in simplifying the square root are listed below.
