Simplify Square Root of 78768

Here we will show you two methods that you can use to simplify the square root of 78768. In other words, we will show you how to find the square root of 78768 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.

√78768 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78768 to simplify the square root of 78768. 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 78768. The factors of 78768 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 547, 1094, 1641, 2188, 3282, 4376, 4923, 6564, 8752, 9846, 13128, 19692, 26256, 39384, and 78768. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 78768 divided by the greatest perfect square from the list of all factors of 78768. We determined above that the greatest perfect square from the list of all factors of 78768 is 144. Furthermore, 78768 divided by 144 is 547, therefore B equals 547.

Now we have A and B and can get our answer to 78768 in its simplest radical form as follows:

√78768 = A√B

√78768 = 12√547

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78768 to simplify the square root of 78768 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 78768 and then take the square root of that product. The prime factors that multiply together to make 78768 are 2 x 2 x 2 x 2 x 3 x 3 x 547. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 78768 by the number (A) squared. 12 squared is 144 and 78768 divided by 144 is 547. Therefore, B equals 547.

Once again we have A and B and can get our answer to 78768 in its simplest radical form as follows:

√78768 = A√B

√78768 = 12√547

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