Simplify Square Root of 420

Here we will show you two methods that you can use to simplify the square root of 420. In other words, we will show you how to find the square root of 420 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√420 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 420 to simplify the square root of 420. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 420. The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 420 divided by the greatest perfect square from the list of all factors of 420. We determined above that the greatest perfect square from the list of all factors of 420 is 4. Furthermore, 420 divided by 4 is 105, therefore B equals 105.

Now we have A and B and can get our answer to 420 in its simplest radical form as follows:

√420 = A√B

√420 = 2√105

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 420 to simplify the square root of 420 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 420 and then take the square root of that product. The prime factors that multiply together to make 420 are 2 x 2 x 3 x 5 x 7. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 420 by the number (A) squared. 2 squared is 4 and 420 divided by 4 is 105. Therefore, B equals 105.

Once again we have A and B and can get our answer to 420 in its simplest radical form as follows:

√420 = A√B

√420 = 2√105

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 421
Here is the next square root on our list that we have simplifed for you.