Simplify Square Root of 32110

Here we will show you two methods that you can use to simplify the square root of 32110. In other words, we will show you how to find the square root of 32110 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.

√32110 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 32110 to simplify the square root of 32110. 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 32110. The factors of 32110 are 1, 2, 5, 10, 13, 19, 26, 38, 65, 95, 130, 169, 190, 247, 338, 494, 845, 1235, 1690, 2470, 3211, 6422, 16055, and 32110. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 32110 divided by the greatest perfect square from the list of all factors of 32110. We determined above that the greatest perfect square from the list of all factors of 32110 is 169. Furthermore, 32110 divided by 169 is 190, therefore B equals 190.

Now we have A and B and can get our answer to 32110 in its simplest radical form as follows:

√32110 = A√B

√32110 = 13√190

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 32110 to simplify the square root of 32110 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 32110 and then take the square root of that product. The prime factors that multiply together to make 32110 are 2 x 5 x 13 x 13 x 19. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 32110 by the number (A) squared. 13 squared is 169 and 32110 divided by 169 is 190. Therefore, B equals 190.

Once again we have A and B and can get our answer to 32110 in its simplest radical form as follows:

√32110 = A√B

√32110 = 13√190

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Simplify Square Root of 32111
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