Simplify Square Root of 33173

Here we will show you two methods that you can use to simplify the square root of 33173. In other words, we will show you how to find the square root of 33173 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.

√33173 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 33173 to simplify the square root of 33173. 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 33173. The factors of 33173 are 1, 7, 49, 677, 4739, and 33173. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 33173 divided by the greatest perfect square from the list of all factors of 33173. We determined above that the greatest perfect square from the list of all factors of 33173 is 49. Furthermore, 33173 divided by 49 is 677, therefore B equals 677.

Now we have A and B and can get our answer to 33173 in its simplest radical form as follows:

√33173 = A√B

√33173 = 7√677

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 33173 to simplify the square root of 33173 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 33173 and then take the square root of that product. The prime factors that multiply together to make 33173 are 7 x 7 x 677. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 33173 by the number (A) squared. 7 squared is 49 and 33173 divided by 49 is 677. Therefore, B equals 677.

Once again we have A and B and can get our answer to 33173 in its simplest radical form as follows:

√33173 = A√B

√33173 = 7√677

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Simplify Square Root of 33174
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