Simplify Square Root of 43776

Here we will show you two methods that you can use to simplify the square root of 43776. In other words, we will show you how to find the square root of 43776 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.

√43776 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 43776 to simplify the square root of 43776. 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 43776. The factors of 43776 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 32, 36, 38, 48, 57, 64, 72, 76, 96, 114, 128, 144, 152, 171, 192, 228, 256, 288, 304, 342, 384, 456, 576, 608, 684, 768, 912, 1152, 1216, 1368, 1824, 2304, 2432, 2736, 3648, 4864, 5472, 7296, 10944, 14592, 21888, and 43776. Furthermore, the greatest perfect square on this list is 2304 and the square root of 2304 is 48. Therefore, A equals 48.

B = Calculate 43776 divided by the greatest perfect square from the list of all factors of 43776. We determined above that the greatest perfect square from the list of all factors of 43776 is 2304. Furthermore, 43776 divided by 2304 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 43776 in its simplest radical form as follows:

√43776 = A√B

√43776 = 48√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 43776 to simplify the square root of 43776 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 43776 and then take the square root of that product. The prime factors that multiply together to make 43776 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 19. 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 3 x 3 = 2304 and the square root of 2304 is 48. Therefore, A equals 48.

B = Divide 43776 by the number (A) squared. 48 squared is 2304 and 43776 divided by 2304 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 43776 in its simplest radical form as follows:

√43776 = A√B

√43776 = 48√19

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Simplify Square Root of 43777
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