Simplify Square Root of 3174

Here we will show you two methods that you can use to simplify the square root of 3174. In other words, we will show you how to find the square root of 3174 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.

√3174 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 3174 to simplify the square root of 3174. 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 3174. The factors of 3174 are 1, 2, 3, 6, 23, 46, 69, 138, 529, 1058, 1587, and 3174. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 3174 divided by the greatest perfect square from the list of all factors of 3174. We determined above that the greatest perfect square from the list of all factors of 3174 is 529. Furthermore, 3174 divided by 529 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 3174 in its simplest radical form as follows:

√3174 = A√B

√3174 = 23√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 3174 to simplify the square root of 3174 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 3174 and then take the square root of that product. The prime factors that multiply together to make 3174 are 2 x 3 x 23 x 23. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 3174 by the number (A) squared. 23 squared is 529 and 3174 divided by 529 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 3174 in its simplest radical form as follows:

√3174 = A√B

√3174 = 23√6

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