Simplify Square Root of 40172

Here we will show you two methods that you can use to simplify the square root of 40172. In other words, we will show you how to find the square root of 40172 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.

√40172 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 40172 to simplify the square root of 40172. 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 40172. The factors of 40172 are 1, 2, 4, 11, 22, 44, 83, 121, 166, 242, 332, 484, 913, 1826, 3652, 10043, 20086, and 40172. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 40172 divided by the greatest perfect square from the list of all factors of 40172. We determined above that the greatest perfect square from the list of all factors of 40172 is 484. Furthermore, 40172 divided by 484 is 83, therefore B equals 83.

Now we have A and B and can get our answer to 40172 in its simplest radical form as follows:

√40172 = A√B

√40172 = 22√83

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 40172 to simplify the square root of 40172 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 40172 and then take the square root of that product. The prime factors that multiply together to make 40172 are 2 x 2 x 11 x 11 x 83. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 40172 by the number (A) squared. 22 squared is 484 and 40172 divided by 484 is 83. Therefore, B equals 83.

Once again we have A and B and can get our answer to 40172 in its simplest radical form as follows:

√40172 = A√B

√40172 = 22√83

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Simplify Square Root of 40173
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