Simplify Square Root of 44736

Here we will show you two methods that you can use to simplify the square root of 44736. In other words, we will show you how to find the square root of 44736 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.

√44736 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 44736 to simplify the square root of 44736. 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 44736. The factors of 44736 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 233, 466, 699, 932, 1398, 1864, 2796, 3728, 5592, 7456, 11184, 14912, 22368, and 44736. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 44736 divided by the greatest perfect square from the list of all factors of 44736. We determined above that the greatest perfect square from the list of all factors of 44736 is 64. Furthermore, 44736 divided by 64 is 699, therefore B equals 699.

Now we have A and B and can get our answer to 44736 in its simplest radical form as follows:

√44736 = A√B

√44736 = 8√699

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 44736 to simplify the square root of 44736 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 44736 and then take the square root of that product. The prime factors that multiply together to make 44736 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 233. 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 44736 by the number (A) squared. 8 squared is 64 and 44736 divided by 64 is 699. Therefore, B equals 699.

Once again we have A and B and can get our answer to 44736 in its simplest radical form as follows:

√44736 = A√B

√44736 = 8√699

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Simplify Square Root of 44737
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