Simplify Square Root of 75936

Here we will show you two methods that you can use to simplify the square root of 75936. In other words, we will show you how to find the square root of 75936 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.

√75936 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75936 to simplify the square root of 75936. 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 75936. The factors of 75936 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 113, 168, 224, 226, 336, 339, 452, 672, 678, 791, 904, 1356, 1582, 1808, 2373, 2712, 3164, 3616, 4746, 5424, 6328, 9492, 10848, 12656, 18984, 25312, 37968, and 75936. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 75936 divided by the greatest perfect square from the list of all factors of 75936. We determined above that the greatest perfect square from the list of all factors of 75936 is 16. Furthermore, 75936 divided by 16 is 4746, therefore B equals 4746.

Now we have A and B and can get our answer to 75936 in its simplest radical form as follows:

√75936 = A√B

√75936 = 4√4746

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75936 to simplify the square root of 75936 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 75936 and then take the square root of that product. The prime factors that multiply together to make 75936 are 2 x 2 x 2 x 2 x 2 x 3 x 7 x 113. 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 75936 by the number (A) squared. 4 squared is 16 and 75936 divided by 16 is 4746. Therefore, B equals 4746.

Once again we have A and B and can get our answer to 75936 in its simplest radical form as follows:

√75936 = A√B

√75936 = 4√4746

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