Simplify Square Root of 57148

Here we will show you two methods that you can use to simplify the square root of 57148. In other words, we will show you how to find the square root of 57148 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.

√57148 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57148 to simplify the square root of 57148. 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 57148. The factors of 57148 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 157, 182, 314, 364, 628, 1099, 2041, 2198, 4082, 4396, 8164, 14287, 28574, and 57148. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 57148 divided by the greatest perfect square from the list of all factors of 57148. We determined above that the greatest perfect square from the list of all factors of 57148 is 4. Furthermore, 57148 divided by 4 is 14287, therefore B equals 14287.

Now we have A and B and can get our answer to 57148 in its simplest radical form as follows:

√57148 = A√B

√57148 = 2√14287

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57148 to simplify the square root of 57148 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 57148 and then take the square root of that product. The prime factors that multiply together to make 57148 are 2 x 2 x 7 x 13 x 157. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 57148 by the number (A) squared. 2 squared is 4 and 57148 divided by 4 is 14287. Therefore, B equals 14287.

Once again we have A and B and can get our answer to 57148 in its simplest radical form as follows:

√57148 = A√B

√57148 = 2√14287

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