Simplify Square Root of 53138

Here we will show you two methods that you can use to simplify the square root of 53138. In other words, we will show you how to find the square root of 53138 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.

√53138 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53138 to simplify the square root of 53138. 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 53138. The factors of 53138 are 1, 2, 163, 326, 26569, and 53138. Furthermore, the greatest perfect square on this list is 26569 and the square root of 26569 is 163. Therefore, A equals 163.

B = Calculate 53138 divided by the greatest perfect square from the list of all factors of 53138. We determined above that the greatest perfect square from the list of all factors of 53138 is 26569. Furthermore, 53138 divided by 26569 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 53138 in its simplest radical form as follows:

√53138 = A√B

√53138 = 163√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53138 to simplify the square root of 53138 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 53138 and then take the square root of that product. The prime factors that multiply together to make 53138 are 2 x 163 x 163. When we strip out the pairs only, we get 163 x 163 = 26569 and the square root of 26569 is 163. Therefore, A equals 163.

B = Divide 53138 by the number (A) squared. 163 squared is 26569 and 53138 divided by 26569 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 53138 in its simplest radical form as follows:

√53138 = A√B

√53138 = 163√2

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Simplify Square Root of 53139
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