Simplify Square Root of 89042

Here we will show you two methods that you can use to simplify the square root of 89042. In other words, we will show you how to find the square root of 89042 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.

√89042 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89042 to simplify the square root of 89042. 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 89042. The factors of 89042 are 1, 2, 211, 422, 44521, and 89042. Furthermore, the greatest perfect square on this list is 44521 and the square root of 44521 is 211. Therefore, A equals 211.

B = Calculate 89042 divided by the greatest perfect square from the list of all factors of 89042. We determined above that the greatest perfect square from the list of all factors of 89042 is 44521. Furthermore, 89042 divided by 44521 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 89042 in its simplest radical form as follows:

√89042 = A√B

√89042 = 211√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89042 to simplify the square root of 89042 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 89042 and then take the square root of that product. The prime factors that multiply together to make 89042 are 2 x 211 x 211. When we strip out the pairs only, we get 211 x 211 = 44521 and the square root of 44521 is 211. Therefore, A equals 211.

B = Divide 89042 by the number (A) squared. 211 squared is 44521 and 89042 divided by 44521 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 89042 in its simplest radical form as follows:

√89042 = A√B

√89042 = 211√2

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Simplify Square Root of 89043
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