Simplify Square Root of 63845

Here we will show you two methods that you can use to simplify the square root of 63845. In other words, we will show you how to find the square root of 63845 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.

√63845 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63845 to simplify the square root of 63845. 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 63845. The factors of 63845 are 1, 5, 113, 565, 12769, and 63845. Furthermore, the greatest perfect square on this list is 12769 and the square root of 12769 is 113. Therefore, A equals 113.

B = Calculate 63845 divided by the greatest perfect square from the list of all factors of 63845. We determined above that the greatest perfect square from the list of all factors of 63845 is 12769. Furthermore, 63845 divided by 12769 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 63845 in its simplest radical form as follows:

√63845 = A√B

√63845 = 113√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63845 to simplify the square root of 63845 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 63845 and then take the square root of that product. The prime factors that multiply together to make 63845 are 5 x 113 x 113. When we strip out the pairs only, we get 113 x 113 = 12769 and the square root of 12769 is 113. Therefore, A equals 113.

B = Divide 63845 by the number (A) squared. 113 squared is 12769 and 63845 divided by 12769 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 63845 in its simplest radical form as follows:

√63845 = A√B

√63845 = 113√5

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