Simplify Square Root of 66416

Here we will show you two methods that you can use to simplify the square root of 66416. In other words, we will show you how to find the square root of 66416 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.

√66416 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66416 to simplify the square root of 66416. 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 66416. The factors of 66416 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 593, 1186, 2372, 4151, 4744, 8302, 9488, 16604, 33208, and 66416. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 66416 divided by the greatest perfect square from the list of all factors of 66416. We determined above that the greatest perfect square from the list of all factors of 66416 is 16. Furthermore, 66416 divided by 16 is 4151, therefore B equals 4151.

Now we have A and B and can get our answer to 66416 in its simplest radical form as follows:

√66416 = A√B

√66416 = 4√4151

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66416 to simplify the square root of 66416 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 66416 and then take the square root of that product. The prime factors that multiply together to make 66416 are 2 x 2 x 2 x 2 x 7 x 593. 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 66416 by the number (A) squared. 4 squared is 16 and 66416 divided by 16 is 4151. Therefore, B equals 4151.

Once again we have A and B and can get our answer to 66416 in its simplest radical form as follows:

√66416 = A√B

√66416 = 4√4151

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