Simplify Square Root of 57425

Here we will show you two methods that you can use to simplify the square root of 57425. In other words, we will show you how to find the square root of 57425 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.

√57425 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57425 to simplify the square root of 57425. 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 57425. The factors of 57425 are 1, 5, 25, 2297, 11485, and 57425. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 57425 divided by the greatest perfect square from the list of all factors of 57425. We determined above that the greatest perfect square from the list of all factors of 57425 is 25. Furthermore, 57425 divided by 25 is 2297, therefore B equals 2297.

Now we have A and B and can get our answer to 57425 in its simplest radical form as follows:

√57425 = A√B

√57425 = 5√2297

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57425 to simplify the square root of 57425 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 57425 and then take the square root of that product. The prime factors that multiply together to make 57425 are 5 x 5 x 2297. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 57425 by the number (A) squared. 5 squared is 25 and 57425 divided by 25 is 2297. Therefore, B equals 2297.

Once again we have A and B and can get our answer to 57425 in its simplest radical form as follows:

√57425 = A√B

√57425 = 5√2297

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Simplify Square Root of 57426
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