Simplify Square Root of 69632

Here we will show you two methods that you can use to simplify the square root of 69632. In other words, we will show you how to find the square root of 69632 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.

√69632 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69632 to simplify the square root of 69632. 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 69632. The factors of 69632 are 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 256, 272, 512, 544, 1024, 1088, 2048, 2176, 4096, 4352, 8704, 17408, 34816, and 69632. Furthermore, the greatest perfect square on this list is 4096 and the square root of 4096 is 64. Therefore, A equals 64.

B = Calculate 69632 divided by the greatest perfect square from the list of all factors of 69632. We determined above that the greatest perfect square from the list of all factors of 69632 is 4096. Furthermore, 69632 divided by 4096 is 17, therefore B equals 17.

Now we have A and B and can get our answer to 69632 in its simplest radical form as follows:

√69632 = A√B

√69632 = 64√17

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69632 to simplify the square root of 69632 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 69632 and then take the square root of that product. The prime factors that multiply together to make 69632 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 4096 and the square root of 4096 is 64. Therefore, A equals 64.

B = Divide 69632 by the number (A) squared. 64 squared is 4096 and 69632 divided by 4096 is 17. Therefore, B equals 17.

Once again we have A and B and can get our answer to 69632 in its simplest radical form as follows:

√69632 = A√B

√69632 = 64√17

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