Simplify Square Root of 53235

Here we will show you two methods that you can use to simplify the square root of 53235. In other words, we will show you how to find the square root of 53235 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.

√53235 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53235 to simplify the square root of 53235. 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 53235. The factors of 53235 are 1, 3, 5, 7, 9, 13, 15, 21, 35, 39, 45, 63, 65, 91, 105, 117, 169, 195, 273, 315, 455, 507, 585, 819, 845, 1183, 1365, 1521, 2535, 3549, 4095, 5915, 7605, 10647, 17745, and 53235. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 53235 divided by the greatest perfect square from the list of all factors of 53235. We determined above that the greatest perfect square from the list of all factors of 53235 is 1521. Furthermore, 53235 divided by 1521 is 35, therefore B equals 35.

Now we have A and B and can get our answer to 53235 in its simplest radical form as follows:

√53235 = A√B

√53235 = 39√35

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53235 to simplify the square root of 53235 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 53235 and then take the square root of that product. The prime factors that multiply together to make 53235 are 3 x 3 x 5 x 7 x 13 x 13. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 53235 by the number (A) squared. 39 squared is 1521 and 53235 divided by 1521 is 35. Therefore, B equals 35.

Once again we have A and B and can get our answer to 53235 in its simplest radical form as follows:

√53235 = A√B

√53235 = 39√35

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