Simplify Square Root of 52208

Here we will show you two methods that you can use to simplify the square root of 52208. In other words, we will show you how to find the square root of 52208 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.

√52208 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52208 to simplify the square root of 52208. 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 52208. The factors of 52208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208, 251, 502, 1004, 2008, 3263, 4016, 6526, 13052, 26104, and 52208. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 52208 divided by the greatest perfect square from the list of all factors of 52208. We determined above that the greatest perfect square from the list of all factors of 52208 is 16. Furthermore, 52208 divided by 16 is 3263, therefore B equals 3263.

Now we have A and B and can get our answer to 52208 in its simplest radical form as follows:

√52208 = A√B

√52208 = 4√3263

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52208 to simplify the square root of 52208 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 52208 and then take the square root of that product. The prime factors that multiply together to make 52208 are 2 x 2 x 2 x 2 x 13 x 251. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 52208 by the number (A) squared. 4 squared is 16 and 52208 divided by 16 is 3263. Therefore, B equals 3263.

Once again we have A and B and can get our answer to 52208 in its simplest radical form as follows:

√52208 = A√B

√52208 = 4√3263

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Simplify Square Root of 52209
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