Simplify Square Root of 78720

Here we will show you two methods that you can use to simplify the square root of 78720. In other words, we will show you how to find the square root of 78720 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.

√78720 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78720 to simplify the square root of 78720. 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 78720. The factors of 78720 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 41, 48, 60, 64, 80, 82, 96, 120, 123, 128, 160, 164, 192, 205, 240, 246, 320, 328, 384, 410, 480, 492, 615, 640, 656, 820, 960, 984, 1230, 1312, 1640, 1920, 1968, 2460, 2624, 3280, 3936, 4920, 5248, 6560, 7872, 9840, 13120, 15744, 19680, 26240, 39360, and 78720. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 78720 divided by the greatest perfect square from the list of all factors of 78720. We determined above that the greatest perfect square from the list of all factors of 78720 is 64. Furthermore, 78720 divided by 64 is 1230, therefore B equals 1230.

Now we have A and B and can get our answer to 78720 in its simplest radical form as follows:

√78720 = A√B

√78720 = 8√1230

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78720 to simplify the square root of 78720 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 78720 and then take the square root of that product. The prime factors that multiply together to make 78720 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 41. 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 78720 by the number (A) squared. 8 squared is 64 and 78720 divided by 64 is 1230. Therefore, B equals 1230.

Once again we have A and B and can get our answer to 78720 in its simplest radical form as follows:

√78720 = A√B

√78720 = 8√1230

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Simplify Square Root of 78721
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