Simplify Square Root of 75968

Here we will show you two methods that you can use to simplify the square root of 75968. In other words, we will show you how to find the square root of 75968 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.

√75968 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75968 to simplify the square root of 75968. 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 75968. The factors of 75968 are 1, 2, 4, 8, 16, 32, 64, 1187, 2374, 4748, 9496, 18992, 37984, and 75968. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 75968 divided by the greatest perfect square from the list of all factors of 75968. We determined above that the greatest perfect square from the list of all factors of 75968 is 64. Furthermore, 75968 divided by 64 is 1187, therefore B equals 1187.

Now we have A and B and can get our answer to 75968 in its simplest radical form as follows:

√75968 = A√B

√75968 = 8√1187

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75968 to simplify the square root of 75968 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 75968 and then take the square root of that product. The prime factors that multiply together to make 75968 are 2 x 2 x 2 x 2 x 2 x 2 x 1187. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 75968 by the number (A) squared. 8 squared is 64 and 75968 divided by 64 is 1187. Therefore, B equals 1187.

Once again we have A and B and can get our answer to 75968 in its simplest radical form as follows:

√75968 = A√B

√75968 = 8√1187

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Simplify Square Root of 75969
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