Simplify Square Root of 37632

Here we will show you two methods that you can use to simplify the square root of 37632. In other words, we will show you how to find the square root of 37632 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.

√37632 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 37632 to simplify the square root of 37632. 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 37632. The factors of 37632 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 49, 56, 64, 84, 96, 98, 112, 128, 147, 168, 192, 196, 224, 256, 294, 336, 384, 392, 448, 588, 672, 768, 784, 896, 1176, 1344, 1568, 1792, 2352, 2688, 3136, 4704, 5376, 6272, 9408, 12544, 18816, and 37632. Furthermore, the greatest perfect square on this list is 12544 and the square root of 12544 is 112. Therefore, A equals 112.

B = Calculate 37632 divided by the greatest perfect square from the list of all factors of 37632. We determined above that the greatest perfect square from the list of all factors of 37632 is 12544. Furthermore, 37632 divided by 12544 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 37632 in its simplest radical form as follows:

√37632 = A√B

√37632 = 112√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 37632 to simplify the square root of 37632 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 37632 and then take the square root of that product. The prime factors that multiply together to make 37632 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 7. 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 7 x 7 = 12544 and the square root of 12544 is 112. Therefore, A equals 112.

B = Divide 37632 by the number (A) squared. 112 squared is 12544 and 37632 divided by 12544 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 37632 in its simplest radical form as follows:

√37632 = A√B

√37632 = 112√3

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Simplify Square Root of 37633
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