Simplify Square Root of 61803

Here we will show you two methods that you can use to simplify the square root of 61803. In other words, we will show you how to find the square root of 61803 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.

√61803 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 61803 to simplify the square root of 61803. 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 61803. The factors of 61803 are 1, 3, 7, 9, 21, 27, 63, 81, 109, 189, 327, 567, 763, 981, 2289, 2943, 6867, 8829, 20601, and 61803. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 61803 divided by the greatest perfect square from the list of all factors of 61803. We determined above that the greatest perfect square from the list of all factors of 61803 is 81. Furthermore, 61803 divided by 81 is 763, therefore B equals 763.

Now we have A and B and can get our answer to 61803 in its simplest radical form as follows:

√61803 = A√B

√61803 = 9√763

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 61803 to simplify the square root of 61803 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 61803 and then take the square root of that product. The prime factors that multiply together to make 61803 are 3 x 3 x 3 x 3 x 7 x 109. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 61803 by the number (A) squared. 9 squared is 81 and 61803 divided by 81 is 763. Therefore, B equals 763.

Once again we have A and B and can get our answer to 61803 in its simplest radical form as follows:

√61803 = A√B

√61803 = 9√763

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