Simplify Square Root of 57291

Here we will show you two methods that you can use to simplify the square root of 57291. In other words, we will show you how to find the square root of 57291 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.

√57291 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57291 to simplify the square root of 57291. 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 57291. The factors of 57291 are 1, 3, 13, 39, 113, 169, 339, 507, 1469, 4407, 19097, and 57291. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 57291 divided by the greatest perfect square from the list of all factors of 57291. We determined above that the greatest perfect square from the list of all factors of 57291 is 169. Furthermore, 57291 divided by 169 is 339, therefore B equals 339.

Now we have A and B and can get our answer to 57291 in its simplest radical form as follows:

√57291 = A√B

√57291 = 13√339

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57291 to simplify the square root of 57291 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 57291 and then take the square root of that product. The prime factors that multiply together to make 57291 are 3 x 13 x 13 x 113. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 57291 by the number (A) squared. 13 squared is 169 and 57291 divided by 169 is 339. Therefore, B equals 339.

Once again we have A and B and can get our answer to 57291 in its simplest radical form as follows:

√57291 = A√B

√57291 = 13√339

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Simplify Square Root of 57292
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