Simplify Square Root of 21632

Here we will show you two methods that you can use to simplify the square root of 21632. In other words, we will show you how to find the square root of 21632 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.

√21632 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 21632 to simplify the square root of 21632. 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 21632. The factors of 21632 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 169, 208, 338, 416, 676, 832, 1352, 1664, 2704, 5408, 10816, and 21632. Furthermore, the greatest perfect square on this list is 10816 and the square root of 10816 is 104. Therefore, A equals 104.

B = Calculate 21632 divided by the greatest perfect square from the list of all factors of 21632. We determined above that the greatest perfect square from the list of all factors of 21632 is 10816. Furthermore, 21632 divided by 10816 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 21632 in its simplest radical form as follows:

√21632 = A√B

√21632 = 104√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 21632 to simplify the square root of 21632 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 21632 and then take the square root of that product. The prime factors that multiply together to make 21632 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 13 x 13 = 10816 and the square root of 10816 is 104. Therefore, A equals 104.

B = Divide 21632 by the number (A) squared. 104 squared is 10816 and 21632 divided by 10816 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 21632 in its simplest radical form as follows:

√21632 = A√B

√21632 = 104√2

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Simplify Square Root of 21633
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