Simplify Square Root of 57188

Here we will show you two methods that you can use to simplify the square root of 57188. In other words, we will show you how to find the square root of 57188 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.

√57188 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57188 to simplify the square root of 57188. 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 57188. The factors of 57188 are 1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 841, 986, 1682, 1972, 3364, 14297, 28594, and 57188. Furthermore, the greatest perfect square on this list is 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Calculate 57188 divided by the greatest perfect square from the list of all factors of 57188. We determined above that the greatest perfect square from the list of all factors of 57188 is 3364. Furthermore, 57188 divided by 3364 is 17, therefore B equals 17.

Now we have A and B and can get our answer to 57188 in its simplest radical form as follows:

√57188 = A√B

√57188 = 58√17

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57188 to simplify the square root of 57188 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 57188 and then take the square root of that product. The prime factors that multiply together to make 57188 are 2 x 2 x 17 x 29 x 29. When we strip out the pairs only, we get 2 x 2 x 29 x 29 = 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Divide 57188 by the number (A) squared. 58 squared is 3364 and 57188 divided by 3364 is 17. Therefore, B equals 17.

Once again we have A and B and can get our answer to 57188 in its simplest radical form as follows:

√57188 = A√B

√57188 = 58√17

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Simplify Square Root of 57189
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