Simplify Square Root of 2675

Here we will show you two methods that you can use to simplify the square root of 2675. In other words, we will show you how to find the square root of 2675 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.

√2675 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2675 to simplify the square root of 2675. 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 2675. The factors of 2675 are 1, 5, 25, 107, 535, and 2675. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 2675 divided by the greatest perfect square from the list of all factors of 2675. We determined above that the greatest perfect square from the list of all factors of 2675 is 25. Furthermore, 2675 divided by 25 is 107, therefore B equals 107.

Now we have A and B and can get our answer to 2675 in its simplest radical form as follows:

√2675 = A√B

√2675 = 5√107

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2675 to simplify the square root of 2675 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 2675 and then take the square root of that product. The prime factors that multiply together to make 2675 are 5 x 5 x 107. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 2675 by the number (A) squared. 5 squared is 25 and 2675 divided by 25 is 107. Therefore, B equals 107.

Once again we have A and B and can get our answer to 2675 in its simplest radical form as follows:

√2675 = A√B

√2675 = 5√107

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