Simplify Square Root of 64208

Here we will show you two methods that you can use to simplify the square root of 64208. In other words, we will show you how to find the square root of 64208 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.

√64208 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 64208 to simplify the square root of 64208. 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 64208. The factors of 64208 are 1, 2, 4, 8, 16, 4013, 8026, 16052, 32104, and 64208. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 64208 divided by the greatest perfect square from the list of all factors of 64208. We determined above that the greatest perfect square from the list of all factors of 64208 is 16. Furthermore, 64208 divided by 16 is 4013, therefore B equals 4013.

Now we have A and B and can get our answer to 64208 in its simplest radical form as follows:

√64208 = A√B

√64208 = 4√4013

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 64208 to simplify the square root of 64208 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 64208 and then take the square root of that product. The prime factors that multiply together to make 64208 are 2 x 2 x 2 x 2 x 4013. 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 64208 by the number (A) squared. 4 squared is 16 and 64208 divided by 16 is 4013. Therefore, B equals 4013.

Once again we have A and B and can get our answer to 64208 in its simplest radical form as follows:

√64208 = A√B

√64208 = 4√4013

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Simplify Square Root of 64209
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