Simplify Square Root of 43923

Here we will show you two methods that you can use to simplify the square root of 43923. In other words, we will show you how to find the square root of 43923 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.

√43923 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43923 to simplify the square root of 43923. 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 43923. The factors of 43923 are 1, 3, 11, 33, 121, 363, 1331, 3993, 14641, and 43923. Furthermore, the greatest perfect square on this list is 14641 and the square root of 14641 is 121. Therefore, A equals 121.

B = Calculate 43923 divided by the greatest perfect square from the list of all factors of 43923. We determined above that the greatest perfect square from the list of all factors of 43923 is 14641. Furthermore, 43923 divided by 14641 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 43923 in its simplest radical form as follows:

√43923 = A√B

√43923 = 121√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43923 to simplify the square root of 43923 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 43923 and then take the square root of that product. The prime factors that multiply together to make 43923 are 3 x 11 x 11 x 11 x 11. When we strip out the pairs only, we get 11 x 11 x 11 x 11 = 14641 and the square root of 14641 is 121. Therefore, A equals 121.

B = Divide 43923 by the number (A) squared. 121 squared is 14641 and 43923 divided by 14641 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 43923 in its simplest radical form as follows:

√43923 = A√B

√43923 = 121√3

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Simplify Square Root of 43924
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