Simplify Square Root of 57245

Here we will show you two methods that you can use to simplify the square root of 57245. In other words, we will show you how to find the square root of 57245 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.

√57245 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57245 to simplify the square root of 57245. 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 57245. The factors of 57245 are 1, 5, 107, 535, 11449, and 57245. Furthermore, the greatest perfect square on this list is 11449 and the square root of 11449 is 107. Therefore, A equals 107.

B = Calculate 57245 divided by the greatest perfect square from the list of all factors of 57245. We determined above that the greatest perfect square from the list of all factors of 57245 is 11449. Furthermore, 57245 divided by 11449 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 57245 in its simplest radical form as follows:

√57245 = A√B

√57245 = 107√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57245 to simplify the square root of 57245 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 57245 and then take the square root of that product. The prime factors that multiply together to make 57245 are 5 x 107 x 107. When we strip out the pairs only, we get 107 x 107 = 11449 and the square root of 11449 is 107. Therefore, A equals 107.

B = Divide 57245 by the number (A) squared. 107 squared is 11449 and 57245 divided by 11449 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 57245 in its simplest radical form as follows:

√57245 = A√B

√57245 = 107√5

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Simplify Square Root of 57246
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