Simplify Square Root of 41772

Here we will show you two methods that you can use to simplify the square root of 41772. In other words, we will show you how to find the square root of 41772 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.

√41772 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 41772 to simplify the square root of 41772. 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 41772. The factors of 41772 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708, 3481, 6962, 10443, 13924, 20886, and 41772. Furthermore, the greatest perfect square on this list is 13924 and the square root of 13924 is 118. Therefore, A equals 118.

B = Calculate 41772 divided by the greatest perfect square from the list of all factors of 41772. We determined above that the greatest perfect square from the list of all factors of 41772 is 13924. Furthermore, 41772 divided by 13924 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 41772 in its simplest radical form as follows:

√41772 = A√B

√41772 = 118√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 41772 to simplify the square root of 41772 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 41772 and then take the square root of that product. The prime factors that multiply together to make 41772 are 2 x 2 x 3 x 59 x 59. When we strip out the pairs only, we get 2 x 2 x 59 x 59 = 13924 and the square root of 13924 is 118. Therefore, A equals 118.

B = Divide 41772 by the number (A) squared. 118 squared is 13924 and 41772 divided by 13924 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 41772 in its simplest radical form as follows:

√41772 = A√B

√41772 = 118√3

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Simplify Square Root of 41773
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