Simplify Square Root of 91852

Here we will show you two methods that you can use to simplify the square root of 91852. In other words, we will show you how to find the square root of 91852 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.

√91852 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 91852 to simplify the square root of 91852. 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 91852. The factors of 91852 are 1, 2, 4, 22963, 45926, and 91852. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 91852 divided by the greatest perfect square from the list of all factors of 91852. We determined above that the greatest perfect square from the list of all factors of 91852 is 4. Furthermore, 91852 divided by 4 is 22963, therefore B equals 22963.

Now we have A and B and can get our answer to 91852 in its simplest radical form as follows:

√91852 = A√B

√91852 = 2√22963

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 91852 to simplify the square root of 91852 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 91852 and then take the square root of that product. The prime factors that multiply together to make 91852 are 2 x 2 x 22963. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 91852 by the number (A) squared. 2 squared is 4 and 91852 divided by 4 is 22963. Therefore, B equals 22963.

Once again we have A and B and can get our answer to 91852 in its simplest radical form as follows:

√91852 = A√B

√91852 = 2√22963

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Simplify Square Root of 91853
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