Simplify Square Root of 89146

Here we will show you two methods that you can use to simplify the square root of 89146. In other words, we will show you how to find the square root of 89146 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.

√89146 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 89146 to simplify the square root of 89146. 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 89146. The factors of 89146 are 1, 2, 29, 53, 58, 106, 841, 1537, 1682, 3074, 44573, and 89146. Furthermore, the greatest perfect square on this list is 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Calculate 89146 divided by the greatest perfect square from the list of all factors of 89146. We determined above that the greatest perfect square from the list of all factors of 89146 is 841. Furthermore, 89146 divided by 841 is 106, therefore B equals 106.

Now we have A and B and can get our answer to 89146 in its simplest radical form as follows:

√89146 = A√B

√89146 = 29√106

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 89146 to simplify the square root of 89146 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 89146 and then take the square root of that product. The prime factors that multiply together to make 89146 are 2 x 29 x 29 x 53. When we strip out the pairs only, we get 29 x 29 = 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Divide 89146 by the number (A) squared. 29 squared is 841 and 89146 divided by 841 is 106. Therefore, B equals 106.

Once again we have A and B and can get our answer to 89146 in its simplest radical form as follows:

√89146 = A√B

√89146 = 29√106

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Simplify Square Root of 89147
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