Simplify Square Root of 17296

Here we will show you two methods that you can use to simplify the square root of 17296. In other words, we will show you how to find the square root of 17296 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.

√17296 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 17296 to simplify the square root of 17296. 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 17296. The factors of 17296 are 1, 2, 4, 8, 16, 23, 46, 47, 92, 94, 184, 188, 368, 376, 752, 1081, 2162, 4324, 8648, and 17296. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 17296 divided by the greatest perfect square from the list of all factors of 17296. We determined above that the greatest perfect square from the list of all factors of 17296 is 16. Furthermore, 17296 divided by 16 is 1081, therefore B equals 1081.

Now we have A and B and can get our answer to 17296 in its simplest radical form as follows:

√17296 = A√B

√17296 = 4√1081

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 17296 to simplify the square root of 17296 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 17296 and then take the square root of that product. The prime factors that multiply together to make 17296 are 2 x 2 x 2 x 2 x 23 x 47. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 17296 by the number (A) squared. 4 squared is 16 and 17296 divided by 16 is 1081. Therefore, B equals 1081.

Once again we have A and B and can get our answer to 17296 in its simplest radical form as follows:

√17296 = A√B

√17296 = 4√1081

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