Simplify Square Root of 74284

Here we will show you two methods that you can use to simplify the square root of 74284. In other words, we will show you how to find the square root of 74284 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.

√74284 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74284 to simplify the square root of 74284. 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 74284. The factors of 74284 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 379, 758, 1516, 2653, 5306, 10612, 18571, 37142, and 74284. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 74284 divided by the greatest perfect square from the list of all factors of 74284. We determined above that the greatest perfect square from the list of all factors of 74284 is 196. Furthermore, 74284 divided by 196 is 379, therefore B equals 379.

Now we have A and B and can get our answer to 74284 in its simplest radical form as follows:

√74284 = A√B

√74284 = 14√379

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74284 to simplify the square root of 74284 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 74284 and then take the square root of that product. The prime factors that multiply together to make 74284 are 2 x 2 x 7 x 7 x 379. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 74284 by the number (A) squared. 14 squared is 196 and 74284 divided by 196 is 379. Therefore, B equals 379.

Once again we have A and B and can get our answer to 74284 in its simplest radical form as follows:

√74284 = A√B

√74284 = 14√379

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Simplify Square Root of 74285
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