Simplify Square Root of 53371

Here we will show you two methods that you can use to simplify the square root of 53371. In other words, we will show you how to find the square root of 53371 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.

√53371 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53371 to simplify the square root of 53371. 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 53371. The factors of 53371 are 1, 19, 53, 1007, 2809, and 53371. Furthermore, the greatest perfect square on this list is 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Calculate 53371 divided by the greatest perfect square from the list of all factors of 53371. We determined above that the greatest perfect square from the list of all factors of 53371 is 2809. Furthermore, 53371 divided by 2809 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 53371 in its simplest radical form as follows:

√53371 = A√B

√53371 = 53√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53371 to simplify the square root of 53371 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 53371 and then take the square root of that product. The prime factors that multiply together to make 53371 are 19 x 53 x 53. When we strip out the pairs only, we get 53 x 53 = 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Divide 53371 by the number (A) squared. 53 squared is 2809 and 53371 divided by 2809 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 53371 in its simplest radical form as follows:

√53371 = A√B

√53371 = 53√19

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Simplify Square Root of 53372
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