Simplify Square Root of 53125

Here we will show you two methods that you can use to simplify the square root of 53125. In other words, we will show you how to find the square root of 53125 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.

√53125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53125 to simplify the square root of 53125. 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 53125. The factors of 53125 are 1, 5, 17, 25, 85, 125, 425, 625, 2125, 3125, 10625, and 53125. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 53125 divided by the greatest perfect square from the list of all factors of 53125. We determined above that the greatest perfect square from the list of all factors of 53125 is 625. Furthermore, 53125 divided by 625 is 85, therefore B equals 85.

Now we have A and B and can get our answer to 53125 in its simplest radical form as follows:

√53125 = A√B

√53125 = 25√85

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53125 to simplify the square root of 53125 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 53125 and then take the square root of that product. The prime factors that multiply together to make 53125 are 5 x 5 x 5 x 5 x 5 x 17. When we strip out the pairs only, we get 5 x 5 x 5 x 5 = 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Divide 53125 by the number (A) squared. 25 squared is 625 and 53125 divided by 625 is 85. Therefore, B equals 85.

Once again we have A and B and can get our answer to 53125 in its simplest radical form as follows:

√53125 = A√B

√53125 = 25√85

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Simplify Square Root of 53126
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