Simplify Square Root of 85054

Here we will show you two methods that you can use to simplify the square root of 85054. In other words, we will show you how to find the square root of 85054 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.

√85054 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85054 to simplify the square root of 85054. 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 85054. The factors of 85054 are 1, 2, 23, 43, 46, 86, 989, 1849, 1978, 3698, 42527, and 85054. Furthermore, the greatest perfect square on this list is 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Calculate 85054 divided by the greatest perfect square from the list of all factors of 85054. We determined above that the greatest perfect square from the list of all factors of 85054 is 1849. Furthermore, 85054 divided by 1849 is 46, therefore B equals 46.

Now we have A and B and can get our answer to 85054 in its simplest radical form as follows:

√85054 = A√B

√85054 = 43√46

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85054 to simplify the square root of 85054 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 85054 and then take the square root of that product. The prime factors that multiply together to make 85054 are 2 x 23 x 43 x 43. When we strip out the pairs only, we get 43 x 43 = 1849 and the square root of 1849 is 43. Therefore, A equals 43.

B = Divide 85054 by the number (A) squared. 43 squared is 1849 and 85054 divided by 1849 is 46. Therefore, B equals 46.

Once again we have A and B and can get our answer to 85054 in its simplest radical form as follows:

√85054 = A√B

√85054 = 43√46

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Simplify Square Root of 85055
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