Simplify Square Root of 21805

Here we will show you two methods that you can use to simplify the square root of 21805. In other words, we will show you how to find the square root of 21805 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.

√21805 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21805 to simplify the square root of 21805. 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 21805. The factors of 21805 are 1, 5, 7, 35, 49, 89, 245, 445, 623, 3115, 4361, and 21805. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 21805 divided by the greatest perfect square from the list of all factors of 21805. We determined above that the greatest perfect square from the list of all factors of 21805 is 49. Furthermore, 21805 divided by 49 is 445, therefore B equals 445.

Now we have A and B and can get our answer to 21805 in its simplest radical form as follows:

√21805 = A√B

√21805 = 7√445

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21805 to simplify the square root of 21805 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 21805 and then take the square root of that product. The prime factors that multiply together to make 21805 are 5 x 7 x 7 x 89. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 21805 by the number (A) squared. 7 squared is 49 and 21805 divided by 49 is 445. Therefore, B equals 445.

Once again we have A and B and can get our answer to 21805 in its simplest radical form as follows:

√21805 = A√B

√21805 = 7√445

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Simplify Square Root of 21806
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