Simplify Square Root of 43907

Here we will show you two methods that you can use to simplify the square root of 43907. In other words, we will show you how to find the square root of 43907 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.

√43907 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43907 to simplify the square root of 43907. 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 43907. The factors of 43907 are 1, 23, 83, 529, 1909, and 43907. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 43907 divided by the greatest perfect square from the list of all factors of 43907. We determined above that the greatest perfect square from the list of all factors of 43907 is 529. Furthermore, 43907 divided by 529 is 83, therefore B equals 83.

Now we have A and B and can get our answer to 43907 in its simplest radical form as follows:

√43907 = A√B

√43907 = 23√83

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43907 to simplify the square root of 43907 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 43907 and then take the square root of that product. The prime factors that multiply together to make 43907 are 23 x 23 x 83. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 43907 by the number (A) squared. 23 squared is 529 and 43907 divided by 529 is 83. Therefore, B equals 83.

Once again we have A and B and can get our answer to 43907 in its simplest radical form as follows:

√43907 = A√B

√43907 = 23√83

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