Simplify Square Root of 58806

Here we will show you two methods that you can use to simplify the square root of 58806. In other words, we will show you how to find the square root of 58806 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.

√58806 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58806 to simplify the square root of 58806. 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 58806. The factors of 58806 are 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 121, 162, 198, 242, 243, 297, 363, 486, 594, 726, 891, 1089, 1782, 2178, 2673, 3267, 5346, 6534, 9801, 19602, 29403, and 58806. Furthermore, the greatest perfect square on this list is 9801 and the square root of 9801 is 99. Therefore, A equals 99.

B = Calculate 58806 divided by the greatest perfect square from the list of all factors of 58806. We determined above that the greatest perfect square from the list of all factors of 58806 is 9801. Furthermore, 58806 divided by 9801 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 58806 in its simplest radical form as follows:

√58806 = A√B

√58806 = 99√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58806 to simplify the square root of 58806 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 58806 and then take the square root of that product. The prime factors that multiply together to make 58806 are 2 x 3 x 3 x 3 x 3 x 3 x 11 x 11. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 11 x 11 = 9801 and the square root of 9801 is 99. Therefore, A equals 99.

B = Divide 58806 by the number (A) squared. 99 squared is 9801 and 58806 divided by 9801 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 58806 in its simplest radical form as follows:

√58806 = A√B

√58806 = 99√6

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