Simplify Square Root of 88806

Here we will show you two methods that you can use to simplify the square root of 88806. In other words, we will show you how to find the square root of 88806 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.

√88806 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 88806 to simplify the square root of 88806. 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 88806. The factors of 88806 are 1, 2, 3, 6, 19, 38, 41, 57, 82, 114, 123, 246, 361, 722, 779, 1083, 1558, 2166, 2337, 4674, 14801, 29602, 44403, and 88806. Furthermore, the greatest perfect square on this list is 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Calculate 88806 divided by the greatest perfect square from the list of all factors of 88806. We determined above that the greatest perfect square from the list of all factors of 88806 is 361. Furthermore, 88806 divided by 361 is 246, therefore B equals 246.

Now we have A and B and can get our answer to 88806 in its simplest radical form as follows:

√88806 = A√B

√88806 = 19√246

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 88806 to simplify the square root of 88806 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 88806 and then take the square root of that product. The prime factors that multiply together to make 88806 are 2 x 3 x 19 x 19 x 41. When we strip out the pairs only, we get 19 x 19 = 361 and the square root of 361 is 19. Therefore, A equals 19.

B = Divide 88806 by the number (A) squared. 19 squared is 361 and 88806 divided by 361 is 246. Therefore, B equals 246.

Once again we have A and B and can get our answer to 88806 in its simplest radical form as follows:

√88806 = A√B

√88806 = 19√246

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Simplify Square Root of 88807
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