Simplify Square Root of 66309

Here we will show you two methods that you can use to simplify the square root of 66309. In other words, we will show you how to find the square root of 66309 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.

√66309 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66309 to simplify the square root of 66309. 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 66309. The factors of 66309 are 1, 3, 23, 31, 69, 93, 713, 961, 2139, 2883, 22103, and 66309. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 66309 divided by the greatest perfect square from the list of all factors of 66309. We determined above that the greatest perfect square from the list of all factors of 66309 is 961. Furthermore, 66309 divided by 961 is 69, therefore B equals 69.

Now we have A and B and can get our answer to 66309 in its simplest radical form as follows:

√66309 = A√B

√66309 = 31√69

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66309 to simplify the square root of 66309 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 66309 and then take the square root of that product. The prime factors that multiply together to make 66309 are 3 x 23 x 31 x 31. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 66309 by the number (A) squared. 31 squared is 961 and 66309 divided by 961 is 69. Therefore, B equals 69.

Once again we have A and B and can get our answer to 66309 in its simplest radical form as follows:

√66309 = A√B

√66309 = 31√69

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