Simplify Square Root of 5796

Here we will show you two methods that you can use to simplify the square root of 5796. In other words, we will show you how to find the square root of 5796 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.

√5796 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 5796 to simplify the square root of 5796. 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 5796. The factors of 5796 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 23, 28, 36, 42, 46, 63, 69, 84, 92, 126, 138, 161, 207, 252, 276, 322, 414, 483, 644, 828, 966, 1449, 1932, 2898, and 5796. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 5796 divided by the greatest perfect square from the list of all factors of 5796. We determined above that the greatest perfect square from the list of all factors of 5796 is 36. Furthermore, 5796 divided by 36 is 161, therefore B equals 161.

Now we have A and B and can get our answer to 5796 in its simplest radical form as follows:

√5796 = A√B

√5796 = 6√161

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 5796 to simplify the square root of 5796 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 5796 and then take the square root of that product. The prime factors that multiply together to make 5796 are 2 x 2 x 3 x 3 x 7 x 23. 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 5796 by the number (A) squared. 6 squared is 36 and 5796 divided by 36 is 161. Therefore, B equals 161.

Once again we have A and B and can get our answer to 5796 in its simplest radical form as follows:

√5796 = A√B

√5796 = 6√161

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