Simplify Square Root of 43648

Here we will show you two methods that you can use to simplify the square root of 43648. In other words, we will show you how to find the square root of 43648 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.

√43648 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43648 to simplify the square root of 43648. 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 43648. The factors of 43648 are 1, 2, 4, 8, 11, 16, 22, 31, 32, 44, 62, 64, 88, 124, 128, 176, 248, 341, 352, 496, 682, 704, 992, 1364, 1408, 1984, 2728, 3968, 5456, 10912, 21824, and 43648. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 43648 divided by the greatest perfect square from the list of all factors of 43648. We determined above that the greatest perfect square from the list of all factors of 43648 is 64. Furthermore, 43648 divided by 64 is 682, therefore B equals 682.

Now we have A and B and can get our answer to 43648 in its simplest radical form as follows:

√43648 = A√B

√43648 = 8√682

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43648 to simplify the square root of 43648 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 43648 and then take the square root of that product. The prime factors that multiply together to make 43648 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 31. 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 43648 by the number (A) squared. 8 squared is 64 and 43648 divided by 64 is 682. Therefore, B equals 682.

Once again we have A and B and can get our answer to 43648 in its simplest radical form as follows:

√43648 = A√B

√43648 = 8√682

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