Simplify Square Root of 43808

Here we will show you two methods that you can use to simplify the square root of 43808. In other words, we will show you how to find the square root of 43808 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.

√43808 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43808 to simplify the square root of 43808. 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 43808. The factors of 43808 are 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592, 1184, 1369, 2738, 5476, 10952, 21904, and 43808. Furthermore, the greatest perfect square on this list is 21904 and the square root of 21904 is 148. Therefore, A equals 148.

B = Calculate 43808 divided by the greatest perfect square from the list of all factors of 43808. We determined above that the greatest perfect square from the list of all factors of 43808 is 21904. Furthermore, 43808 divided by 21904 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 43808 in its simplest radical form as follows:

√43808 = A√B

√43808 = 148√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43808 to simplify the square root of 43808 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 43808 and then take the square root of that product. The prime factors that multiply together to make 43808 are 2 x 2 x 2 x 2 x 2 x 37 x 37. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 37 x 37 = 21904 and the square root of 21904 is 148. Therefore, A equals 148.

B = Divide 43808 by the number (A) squared. 148 squared is 21904 and 43808 divided by 21904 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 43808 in its simplest radical form as follows:

√43808 = A√B

√43808 = 148√2

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Simplify Square Root of 43809
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