Simplify Square Root of 21952

Here we will show you two methods that you can use to simplify the square root of 21952. In other words, we will show you how to find the square root of 21952 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.

√21952 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21952 to simplify the square root of 21952. 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 21952. The factors of 21952 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 343, 392, 448, 686, 784, 1372, 1568, 2744, 3136, 5488, 10976, and 21952. Furthermore, the greatest perfect square on this list is 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Calculate 21952 divided by the greatest perfect square from the list of all factors of 21952. We determined above that the greatest perfect square from the list of all factors of 21952 is 3136. Furthermore, 21952 divided by 3136 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 21952 in its simplest radical form as follows:

√21952 = A√B

√21952 = 56√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21952 to simplify the square root of 21952 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 21952 and then take the square root of that product. The prime factors that multiply together to make 21952 are 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 = 3136 and the square root of 3136 is 56. Therefore, A equals 56.

B = Divide 21952 by the number (A) squared. 56 squared is 3136 and 21952 divided by 3136 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 21952 in its simplest radical form as follows:

√21952 = A√B

√21952 = 56√7

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