Simplify Square Root of 40590

Here we will show you two methods that you can use to simplify the square root of 40590. In other words, we will show you how to find the square root of 40590 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.

√40590 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40590 to simplify the square root of 40590. 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 40590. The factors of 40590 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 41, 45, 55, 66, 82, 90, 99, 110, 123, 165, 198, 205, 246, 330, 369, 410, 451, 495, 615, 738, 902, 990, 1230, 1353, 1845, 2255, 2706, 3690, 4059, 4510, 6765, 8118, 13530, 20295, and 40590. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 40590 divided by the greatest perfect square from the list of all factors of 40590. We determined above that the greatest perfect square from the list of all factors of 40590 is 9. Furthermore, 40590 divided by 9 is 4510, therefore B equals 4510.

Now we have A and B and can get our answer to 40590 in its simplest radical form as follows:

√40590 = A√B

√40590 = 3√4510

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40590 to simplify the square root of 40590 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 40590 and then take the square root of that product. The prime factors that multiply together to make 40590 are 2 x 3 x 3 x 5 x 11 x 41. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 40590 by the number (A) squared. 3 squared is 9 and 40590 divided by 9 is 4510. Therefore, B equals 4510.

Once again we have A and B and can get our answer to 40590 in its simplest radical form as follows:

√40590 = A√B

√40590 = 3√4510

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