Simplify Square Root of 17488

Here we will show you two methods that you can use to simplify the square root of 17488. In other words, we will show you how to find the square root of 17488 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.

√17488 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 17488 to simplify the square root of 17488. 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 17488. The factors of 17488 are 1, 2, 4, 8, 16, 1093, 2186, 4372, 8744, and 17488. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 17488 divided by the greatest perfect square from the list of all factors of 17488. We determined above that the greatest perfect square from the list of all factors of 17488 is 16. Furthermore, 17488 divided by 16 is 1093, therefore B equals 1093.

Now we have A and B and can get our answer to 17488 in its simplest radical form as follows:

√17488 = A√B

√17488 = 4√1093

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 17488 to simplify the square root of 17488 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 17488 and then take the square root of that product. The prime factors that multiply together to make 17488 are 2 x 2 x 2 x 2 x 1093. 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 17488 by the number (A) squared. 4 squared is 16 and 17488 divided by 16 is 1093. Therefore, B equals 1093.

Once again we have A and B and can get our answer to 17488 in its simplest radical form as follows:

√17488 = A√B

√17488 = 4√1093

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