Simplify Square Root of 51744

Here we will show you two methods that you can use to simplify the square root of 51744. In other words, we will show you how to find the square root of 51744 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.

√51744 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51744 to simplify the square root of 51744. 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 51744. The factors of 51744 are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 32, 33, 42, 44, 48, 49, 56, 66, 77, 84, 88, 96, 98, 112, 132, 147, 154, 168, 176, 196, 224, 231, 264, 294, 308, 336, 352, 392, 462, 528, 539, 588, 616, 672, 784, 924, 1056, 1078, 1176, 1232, 1568, 1617, 1848, 2156, 2352, 2464, 3234, 3696, 4312, 4704, 6468, 7392, 8624, 12936, 17248, 25872, and 51744. Furthermore, the greatest perfect square on this list is 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Calculate 51744 divided by the greatest perfect square from the list of all factors of 51744. We determined above that the greatest perfect square from the list of all factors of 51744 is 784. Furthermore, 51744 divided by 784 is 66, therefore B equals 66.

Now we have A and B and can get our answer to 51744 in its simplest radical form as follows:

√51744 = A√B

√51744 = 28√66

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51744 to simplify the square root of 51744 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 51744 and then take the square root of that product. The prime factors that multiply together to make 51744 are 2 x 2 x 2 x 2 x 2 x 3 x 7 x 7 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 7 x 7 = 784 and the square root of 784 is 28. Therefore, A equals 28.

B = Divide 51744 by the number (A) squared. 28 squared is 784 and 51744 divided by 784 is 66. Therefore, B equals 66.

Once again we have A and B and can get our answer to 51744 in its simplest radical form as follows:

√51744 = A√B

√51744 = 28√66

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