Simplify Square Root of 48768

Here we will show you two methods that you can use to simplify the square root of 48768. In other words, we will show you how to find the square root of 48768 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.

√48768 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48768 to simplify the square root of 48768. 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 48768. The factors of 48768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 127, 128, 192, 254, 381, 384, 508, 762, 1016, 1524, 2032, 3048, 4064, 6096, 8128, 12192, 16256, 24384, and 48768. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 48768 divided by the greatest perfect square from the list of all factors of 48768. We determined above that the greatest perfect square from the list of all factors of 48768 is 64. Furthermore, 48768 divided by 64 is 762, therefore B equals 762.

Now we have A and B and can get our answer to 48768 in its simplest radical form as follows:

√48768 = A√B

√48768 = 8√762

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48768 to simplify the square root of 48768 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 48768 and then take the square root of that product. The prime factors that multiply together to make 48768 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 127. 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 48768 by the number (A) squared. 8 squared is 64 and 48768 divided by 64 is 762. Therefore, B equals 762.

Once again we have A and B and can get our answer to 48768 in its simplest radical form as follows:

√48768 = A√B

√48768 = 8√762

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