Simplify Square Root of 71984

Here we will show you two methods that you can use to simplify the square root of 71984. In other words, we will show you how to find the square root of 71984 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.

√71984 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 71984 to simplify the square root of 71984. 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 71984. The factors of 71984 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 409, 818, 1636, 3272, 4499, 6544, 8998, 17996, 35992, and 71984. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 71984 divided by the greatest perfect square from the list of all factors of 71984. We determined above that the greatest perfect square from the list of all factors of 71984 is 16. Furthermore, 71984 divided by 16 is 4499, therefore B equals 4499.

Now we have A and B and can get our answer to 71984 in its simplest radical form as follows:

√71984 = A√B

√71984 = 4√4499

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 71984 to simplify the square root of 71984 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 71984 and then take the square root of that product. The prime factors that multiply together to make 71984 are 2 x 2 x 2 x 2 x 11 x 409. 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 71984 by the number (A) squared. 4 squared is 16 and 71984 divided by 16 is 4499. Therefore, B equals 4499.

Once again we have A and B and can get our answer to 71984 in its simplest radical form as follows:

√71984 = A√B

√71984 = 4√4499

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