Simplify Square Root of 53621

Here we will show you two methods that you can use to simplify the square root of 53621. In other words, we will show you how to find the square root of 53621 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.

√53621 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53621 to simplify the square root of 53621. 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 53621. The factors of 53621 are 1, 29, 43, 1247, 1849, and 53621. Furthermore, the greatest perfect square on this list is 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Calculate 53621 divided by the greatest perfect square from the list of all factors of 53621. We determined above that the greatest perfect square from the list of all factors of 53621 is 1849. Furthermore, 53621 divided by 1849 is 29, therefore B equals 29.

Now we have A and B and can get our answer to 53621 in its simplest radical form as follows:

√53621 = A√B

√53621 = 43√29

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53621 to simplify the square root of 53621 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 53621 and then take the square root of that product. The prime factors that multiply together to make 53621 are 29 x 43 x 43. When we strip out the pairs only, we get 43 x 43 = 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Divide 53621 by the number (A) squared. 43 squared is 1849 and 53621 divided by 1849 is 29. Therefore, B equals 29.

Once again we have A and B and can get our answer to 53621 in its simplest radical form as follows:

√53621 = A√B

√53621 = 43√29

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Simplify Square Root of 53622
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