Simplify Square Root of 89093

Here we will show you two methods that you can use to simplify the square root of 89093. In other words, we will show you how to find the square root of 89093 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.

√89093 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89093 to simplify the square root of 89093. 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 89093. The factors of 89093 are 1, 41, 53, 1681, 2173, and 89093. Furthermore, the greatest perfect square on this list is 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Calculate 89093 divided by the greatest perfect square from the list of all factors of 89093. We determined above that the greatest perfect square from the list of all factors of 89093 is 1681. Furthermore, 89093 divided by 1681 is 53, therefore B equals 53.

Now we have A and B and can get our answer to 89093 in its simplest radical form as follows:

√89093 = A√B

√89093 = 41√53

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89093 to simplify the square root of 89093 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 89093 and then take the square root of that product. The prime factors that multiply together to make 89093 are 41 x 41 x 53. When we strip out the pairs only, we get 41 x 41 = 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Divide 89093 by the number (A) squared. 41 squared is 1681 and 89093 divided by 1681 is 53. Therefore, B equals 53.

Once again we have A and B and can get our answer to 89093 in its simplest radical form as follows:

√89093 = A√B

√89093 = 41√53

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Simplify Square Root of 89094
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