Simplify Square Root of 76800

Here we will show you two methods that you can use to simplify the square root of 76800. In other words, we will show you how to find the square root of 76800 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.

√76800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 76800 to simplify the square root of 76800. 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 76800. The factors of 76800 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 512, 600, 640, 768, 800, 960, 1024, 1200, 1280, 1536, 1600, 1920, 2400, 2560, 3072, 3200, 3840, 4800, 5120, 6400, 7680, 9600, 12800, 15360, 19200, 25600, 38400, and 76800. Furthermore, the greatest perfect square on this list is 25600 and the square root of 25600 is 160. Therefore, A equals 160.

B = Calculate 76800 divided by the greatest perfect square from the list of all factors of 76800. We determined above that the greatest perfect square from the list of all factors of 76800 is 25600. Furthermore, 76800 divided by 25600 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 76800 in its simplest radical form as follows:

√76800 = A√B

√76800 = 160√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 76800 to simplify the square root of 76800 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 76800 and then take the square root of that product. The prime factors that multiply together to make 76800 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 = 25600 and the square root of 25600 is 160. Therefore, A equals 160.

B = Divide 76800 by the number (A) squared. 160 squared is 25600 and 76800 divided by 25600 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 76800 in its simplest radical form as follows:

√76800 = A√B

√76800 = 160√3

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Simplify Square Root of 76801
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