Simplify Square Root of 52371

Here we will show you two methods that you can use to simplify the square root of 52371. In other words, we will show you how to find the square root of 52371 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.

√52371 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52371 to simplify the square root of 52371. 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 52371. The factors of 52371 are 1, 3, 9, 11, 23, 33, 69, 99, 207, 253, 529, 759, 1587, 2277, 4761, 5819, 17457, and 52371. Furthermore, the greatest perfect square on this list is 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Calculate 52371 divided by the greatest perfect square from the list of all factors of 52371. We determined above that the greatest perfect square from the list of all factors of 52371 is 4761. Furthermore, 52371 divided by 4761 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 52371 in its simplest radical form as follows:

√52371 = A√B

√52371 = 69√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52371 to simplify the square root of 52371 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 52371 and then take the square root of that product. The prime factors that multiply together to make 52371 are 3 x 3 x 11 x 23 x 23. When we strip out the pairs only, we get 3 x 3 x 23 x 23 = 4761 and the square root of 4761 is 69. Therefore, A equals 69.

B = Divide 52371 by the number (A) squared. 69 squared is 4761 and 52371 divided by 4761 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 52371 in its simplest radical form as follows:

√52371 = A√B

√52371 = 69√11

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Simplify Square Root of 52372
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