Simplify Square Root of 16605

Here we will show you two methods that you can use to simplify the square root of 16605. In other words, we will show you how to find the square root of 16605 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.

√16605 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 16605 to simplify the square root of 16605. 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 16605. The factors of 16605 are 1, 3, 5, 9, 15, 27, 41, 45, 81, 123, 135, 205, 369, 405, 615, 1107, 1845, 3321, 5535, and 16605. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 16605 divided by the greatest perfect square from the list of all factors of 16605. We determined above that the greatest perfect square from the list of all factors of 16605 is 81. Furthermore, 16605 divided by 81 is 205, therefore B equals 205.

Now we have A and B and can get our answer to 16605 in its simplest radical form as follows:

√16605 = A√B

√16605 = 9√205

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 16605 to simplify the square root of 16605 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 16605 and then take the square root of that product. The prime factors that multiply together to make 16605 are 3 x 3 x 3 x 3 x 5 x 41. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 16605 by the number (A) squared. 9 squared is 81 and 16605 divided by 81 is 205. Therefore, B equals 205.

Once again we have A and B and can get our answer to 16605 in its simplest radical form as follows:

√16605 = A√B

√16605 = 9√205

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Simplify Square Root of 16606
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