Simplify Square Root of 44775

Here we will show you two methods that you can use to simplify the square root of 44775. In other words, we will show you how to find the square root of 44775 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.

√44775 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 44775 to simplify the square root of 44775. 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 44775. The factors of 44775 are 1, 3, 5, 9, 15, 25, 45, 75, 199, 225, 597, 995, 1791, 2985, 4975, 8955, 14925, and 44775. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 44775 divided by the greatest perfect square from the list of all factors of 44775. We determined above that the greatest perfect square from the list of all factors of 44775 is 225. Furthermore, 44775 divided by 225 is 199, therefore B equals 199.

Now we have A and B and can get our answer to 44775 in its simplest radical form as follows:

√44775 = A√B

√44775 = 15√199

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 44775 to simplify the square root of 44775 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 44775 and then take the square root of that product. The prime factors that multiply together to make 44775 are 3 x 3 x 5 x 5 x 199. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 44775 by the number (A) squared. 15 squared is 225 and 44775 divided by 225 is 199. Therefore, B equals 199.

Once again we have A and B and can get our answer to 44775 in its simplest radical form as follows:

√44775 = A√B

√44775 = 15√199

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Simplify Square Root of 44776
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