Simplify Square Root of 45045

Here we will show you two methods that you can use to simplify the square root of 45045. In other words, we will show you how to find the square root of 45045 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.

√45045 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45045 to simplify the square root of 45045. 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 45045. The factors of 45045 are 1, 3, 5, 7, 9, 11, 13, 15, 21, 33, 35, 39, 45, 55, 63, 65, 77, 91, 99, 105, 117, 143, 165, 195, 231, 273, 315, 385, 429, 455, 495, 585, 693, 715, 819, 1001, 1155, 1287, 1365, 2145, 3003, 3465, 4095, 5005, 6435, 9009, 15015, and 45045. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 45045 divided by the greatest perfect square from the list of all factors of 45045. We determined above that the greatest perfect square from the list of all factors of 45045 is 9. Furthermore, 45045 divided by 9 is 5005, therefore B equals 5005.

Now we have A and B and can get our answer to 45045 in its simplest radical form as follows:

√45045 = A√B

√45045 = 3√5005

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45045 to simplify the square root of 45045 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 45045 and then take the square root of that product. The prime factors that multiply together to make 45045 are 3 x 3 x 5 x 7 x 11 x 13. 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 45045 by the number (A) squared. 3 squared is 9 and 45045 divided by 9 is 5005. Therefore, B equals 5005.

Once again we have A and B and can get our answer to 45045 in its simplest radical form as follows:

√45045 = A√B

√45045 = 3√5005

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