Simplify Square Root of 83349

Here we will show you two methods that you can use to simplify the square root of 83349. In other words, we will show you how to find the square root of 83349 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.

√83349 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83349 to simplify the square root of 83349. 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 83349. The factors of 83349 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 243, 343, 441, 567, 1029, 1323, 1701, 3087, 3969, 9261, 11907, 27783, and 83349. Furthermore, the greatest perfect square on this list is 3969 and the square root of 3969 is 63. Therefore, A equals 63.

B = Calculate 83349 divided by the greatest perfect square from the list of all factors of 83349. We determined above that the greatest perfect square from the list of all factors of 83349 is 3969. Furthermore, 83349 divided by 3969 is 21, therefore B equals 21.

Now we have A and B and can get our answer to 83349 in its simplest radical form as follows:

√83349 = A√B

√83349 = 63√21

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83349 to simplify the square root of 83349 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 83349 and then take the square root of that product. The prime factors that multiply together to make 83349 are 3 x 3 x 3 x 3 x 3 x 7 x 7 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 7 x 7 = 3969 and the square root of 3969 is 63. Therefore, A equals 63.

B = Divide 83349 by the number (A) squared. 63 squared is 3969 and 83349 divided by 3969 is 21. Therefore, B equals 21.

Once again we have A and B and can get our answer to 83349 in its simplest radical form as follows:

√83349 = A√B

√83349 = 63√21

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