Simplify Square Root of 45264

Here we will show you two methods that you can use to simplify the square root of 45264. In other words, we will show you how to find the square root of 45264 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.

√45264 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45264 to simplify the square root of 45264. 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 45264. The factors of 45264 are 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 41, 46, 48, 69, 82, 92, 123, 138, 164, 184, 246, 276, 328, 368, 492, 552, 656, 943, 984, 1104, 1886, 1968, 2829, 3772, 5658, 7544, 11316, 15088, 22632, and 45264. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 45264 divided by the greatest perfect square from the list of all factors of 45264. We determined above that the greatest perfect square from the list of all factors of 45264 is 16. Furthermore, 45264 divided by 16 is 2829, therefore B equals 2829.

Now we have A and B and can get our answer to 45264 in its simplest radical form as follows:

√45264 = A√B

√45264 = 4√2829

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45264 to simplify the square root of 45264 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 45264 and then take the square root of that product. The prime factors that multiply together to make 45264 are 2 x 2 x 2 x 2 x 3 x 23 x 41. 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 45264 by the number (A) squared. 4 squared is 16 and 45264 divided by 16 is 2829. Therefore, B equals 2829.

Once again we have A and B and can get our answer to 45264 in its simplest radical form as follows:

√45264 = A√B

√45264 = 4√2829

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