Simplify Square Root of 48884

Here we will show you two methods that you can use to simplify the square root of 48884. In other words, we will show you how to find the square root of 48884 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.

√48884 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48884 to simplify the square root of 48884. 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 48884. The factors of 48884 are 1, 2, 4, 11, 22, 44, 101, 121, 202, 242, 404, 484, 1111, 2222, 4444, 12221, 24442, and 48884. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 48884 divided by the greatest perfect square from the list of all factors of 48884. We determined above that the greatest perfect square from the list of all factors of 48884 is 484. Furthermore, 48884 divided by 484 is 101, therefore B equals 101.

Now we have A and B and can get our answer to 48884 in its simplest radical form as follows:

√48884 = A√B

√48884 = 22√101

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48884 to simplify the square root of 48884 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 48884 and then take the square root of that product. The prime factors that multiply together to make 48884 are 2 x 2 x 11 x 11 x 101. 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 48884 by the number (A) squared. 22 squared is 484 and 48884 divided by 484 is 101. Therefore, B equals 101.

Once again we have A and B and can get our answer to 48884 in its simplest radical form as follows:

√48884 = A√B

√48884 = 22√101

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Simplify Square Root of 48885
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