Simplify Square Root of 68640

Here we will show you two methods that you can use to simplify the square root of 68640. In other words, we will show you how to find the square root of 68640 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.

√68640 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68640 to simplify the square root of 68640. 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 68640. The factors of 68640 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 15, 16, 20, 22, 24, 26, 30, 32, 33, 39, 40, 44, 48, 52, 55, 60, 65, 66, 78, 80, 88, 96, 104, 110, 120, 130, 132, 143, 156, 160, 165, 176, 195, 208, 220, 240, 260, 264, 286, 312, 330, 352, 390, 416, 429, 440, 480, 520, 528, 572, 624, 660, 715, 780, 858, 880, 1040, 1056, 1144, 1248, 1320, 1430, 1560, 1716, 1760, 2080, 2145, 2288, 2640, 2860, 3120, 3432, 4290, 4576, 5280, 5720, 6240, 6864, 8580, 11440, 13728, 17160, 22880, 34320, and 68640. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 68640 divided by the greatest perfect square from the list of all factors of 68640. We determined above that the greatest perfect square from the list of all factors of 68640 is 16. Furthermore, 68640 divided by 16 is 4290, therefore B equals 4290.

Now we have A and B and can get our answer to 68640 in its simplest radical form as follows:

√68640 = A√B

√68640 = 4√4290

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68640 to simplify the square root of 68640 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 68640 and then take the square root of that product. The prime factors that multiply together to make 68640 are 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 68640 by the number (A) squared. 4 squared is 16 and 68640 divided by 16 is 4290. Therefore, B equals 4290.

Once again we have A and B and can get our answer to 68640 in its simplest radical form as follows:

√68640 = A√B

√68640 = 4√4290

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Simplify Square Root of 68641
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