Simplify Square Root of 28033

Here we will show you two methods that you can use to simplify the square root of 28033. In other words, we will show you how to find the square root of 28033 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.

√28033 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 28033 to simplify the square root of 28033. 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 28033. The factors of 28033 are 1, 17, 97, 289, 1649, and 28033. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 28033 divided by the greatest perfect square from the list of all factors of 28033. We determined above that the greatest perfect square from the list of all factors of 28033 is 289. Furthermore, 28033 divided by 289 is 97, therefore B equals 97.

Now we have A and B and can get our answer to 28033 in its simplest radical form as follows:

√28033 = A√B

√28033 = 17√97

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 28033 to simplify the square root of 28033 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 28033 and then take the square root of that product. The prime factors that multiply together to make 28033 are 17 x 17 x 97. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 28033 by the number (A) squared. 17 squared is 289 and 28033 divided by 289 is 97. Therefore, B equals 97.

Once again we have A and B and can get our answer to 28033 in its simplest radical form as follows:

√28033 = A√B

√28033 = 17√97

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Simplify Square Root of 28034
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