Simplify Square Root of 53696

Here we will show you two methods that you can use to simplify the square root of 53696. In other words, we will show you how to find the square root of 53696 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.

√53696 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 53696 to simplify the square root of 53696. 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 53696. The factors of 53696 are 1, 2, 4, 8, 16, 32, 64, 839, 1678, 3356, 6712, 13424, 26848, and 53696. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 53696 divided by the greatest perfect square from the list of all factors of 53696. We determined above that the greatest perfect square from the list of all factors of 53696 is 64. Furthermore, 53696 divided by 64 is 839, therefore B equals 839.

Now we have A and B and can get our answer to 53696 in its simplest radical form as follows:

√53696 = A√B

√53696 = 8√839

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 53696 to simplify the square root of 53696 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 53696 and then take the square root of that product. The prime factors that multiply together to make 53696 are 2 x 2 x 2 x 2 x 2 x 2 x 839. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 53696 by the number (A) squared. 8 squared is 64 and 53696 divided by 64 is 839. Therefore, B equals 839.

Once again we have A and B and can get our answer to 53696 in its simplest radical form as follows:

√53696 = A√B

√53696 = 8√839

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Simplify Square Root of 53697
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