Simplify Square Root of 5216

Here we will show you two methods that you can use to simplify the square root of 5216. In other words, we will show you how to find the square root of 5216 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.

√5216 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 5216 to simplify the square root of 5216. 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 5216. The factors of 5216 are 1, 2, 4, 8, 16, 32, 163, 326, 652, 1304, 2608, and 5216. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 5216 divided by the greatest perfect square from the list of all factors of 5216. We determined above that the greatest perfect square from the list of all factors of 5216 is 16. Furthermore, 5216 divided by 16 is 326, therefore B equals 326.

Now we have A and B and can get our answer to 5216 in its simplest radical form as follows:

√5216 = A√B

√5216 = 4√326

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 5216 to simplify the square root of 5216 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 5216 and then take the square root of that product. The prime factors that multiply together to make 5216 are 2 x 2 x 2 x 2 x 2 x 163. 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 5216 by the number (A) squared. 4 squared is 16 and 5216 divided by 16 is 326. Therefore, B equals 326.

Once again we have A and B and can get our answer to 5216 in its simplest radical form as follows:

√5216 = A√B

√5216 = 4√326

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Simplify Square Root of 5217
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