Simplify Square Root of 52325

Here we will show you two methods that you can use to simplify the square root of 52325. In other words, we will show you how to find the square root of 52325 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.

√52325 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52325 to simplify the square root of 52325. 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 52325. The factors of 52325 are 1, 5, 7, 13, 23, 25, 35, 65, 91, 115, 161, 175, 299, 325, 455, 575, 805, 1495, 2093, 2275, 4025, 7475, 10465, and 52325. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 52325 divided by the greatest perfect square from the list of all factors of 52325. We determined above that the greatest perfect square from the list of all factors of 52325 is 25. Furthermore, 52325 divided by 25 is 2093, therefore B equals 2093.

Now we have A and B and can get our answer to 52325 in its simplest radical form as follows:

√52325 = A√B

√52325 = 5√2093

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52325 to simplify the square root of 52325 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 52325 and then take the square root of that product. The prime factors that multiply together to make 52325 are 5 x 5 x 7 x 13 x 23. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 52325 by the number (A) squared. 5 squared is 25 and 52325 divided by 25 is 2093. Therefore, B equals 2093.

Once again we have A and B and can get our answer to 52325 in its simplest radical form as follows:

√52325 = A√B

√52325 = 5√2093

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