Simplify Square Root of 15660

Here we will show you two methods that you can use to simplify the square root of 15660. In other words, we will show you how to find the square root of 15660 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.

√15660 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 15660 to simplify the square root of 15660. 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 15660. The factors of 15660 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 29, 30, 36, 45, 54, 58, 60, 87, 90, 108, 116, 135, 145, 174, 180, 261, 270, 290, 348, 435, 522, 540, 580, 783, 870, 1044, 1305, 1566, 1740, 2610, 3132, 3915, 5220, 7830, and 15660. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 15660 divided by the greatest perfect square from the list of all factors of 15660. We determined above that the greatest perfect square from the list of all factors of 15660 is 36. Furthermore, 15660 divided by 36 is 435, therefore B equals 435.

Now we have A and B and can get our answer to 15660 in its simplest radical form as follows:

√15660 = A√B

√15660 = 6√435

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 15660 to simplify the square root of 15660 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 15660 and then take the square root of that product. The prime factors that multiply together to make 15660 are 2 x 2 x 3 x 3 x 3 x 5 x 29. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 15660 by the number (A) squared. 6 squared is 36 and 15660 divided by 36 is 435. Therefore, B equals 435.

Once again we have A and B and can get our answer to 15660 in its simplest radical form as follows:

√15660 = A√B

√15660 = 6√435

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