Simplify Square Root of 74191

Here we will show you two methods that you can use to simplify the square root of 74191. In other words, we will show you how to find the square root of 74191 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.

√74191 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74191 to simplify the square root of 74191. 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 74191. The factors of 74191 are 1, 13, 169, 439, 5707, and 74191. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 74191 divided by the greatest perfect square from the list of all factors of 74191. We determined above that the greatest perfect square from the list of all factors of 74191 is 169. Furthermore, 74191 divided by 169 is 439, therefore B equals 439.

Now we have A and B and can get our answer to 74191 in its simplest radical form as follows:

√74191 = A√B

√74191 = 13√439

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74191 to simplify the square root of 74191 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 74191 and then take the square root of that product. The prime factors that multiply together to make 74191 are 13 x 13 x 439. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 74191 by the number (A) squared. 13 squared is 169 and 74191 divided by 169 is 439. Therefore, B equals 439.

Once again we have A and B and can get our answer to 74191 in its simplest radical form as follows:

√74191 = A√B

√74191 = 13√439

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Simplify Square Root of 74192
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