Simplify Square Root of 49852

Here we will show you two methods that you can use to simplify the square root of 49852. In other words, we will show you how to find the square root of 49852 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.

√49852 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49852 to simplify the square root of 49852. 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 49852. The factors of 49852 are 1, 2, 4, 11, 22, 44, 103, 121, 206, 242, 412, 484, 1133, 2266, 4532, 12463, 24926, and 49852. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 49852 divided by the greatest perfect square from the list of all factors of 49852. We determined above that the greatest perfect square from the list of all factors of 49852 is 484. Furthermore, 49852 divided by 484 is 103, therefore B equals 103.

Now we have A and B and can get our answer to 49852 in its simplest radical form as follows:

√49852 = A√B

√49852 = 22√103

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49852 to simplify the square root of 49852 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 49852 and then take the square root of that product. The prime factors that multiply together to make 49852 are 2 x 2 x 11 x 11 x 103. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 49852 by the number (A) squared. 22 squared is 484 and 49852 divided by 484 is 103. Therefore, B equals 103.

Once again we have A and B and can get our answer to 49852 in its simplest radical form as follows:

√49852 = A√B

√49852 = 22√103

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Simplify Square Root of 49853
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