Simplify Square Root of 85529

Here we will show you two methods that you can use to simplify the square root of 85529. In other words, we will show you how to find the square root of 85529 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.

√85529 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85529 to simplify the square root of 85529. 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 85529. The factors of 85529 are 1, 31, 89, 961, 2759, and 85529. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 85529 divided by the greatest perfect square from the list of all factors of 85529. We determined above that the greatest perfect square from the list of all factors of 85529 is 961. Furthermore, 85529 divided by 961 is 89, therefore B equals 89.

Now we have A and B and can get our answer to 85529 in its simplest radical form as follows:

√85529 = A√B

√85529 = 31√89

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85529 to simplify the square root of 85529 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 85529 and then take the square root of that product. The prime factors that multiply together to make 85529 are 31 x 31 x 89. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 85529 by the number (A) squared. 31 squared is 961 and 85529 divided by 961 is 89. Therefore, B equals 89.

Once again we have A and B and can get our answer to 85529 in its simplest radical form as follows:

√85529 = A√B

√85529 = 31√89

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Simplify Square Root of 85530
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