Simplify Square Root of 74034

Here we will show you two methods that you can use to simplify the square root of 74034. In other words, we will show you how to find the square root of 74034 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.

√74034 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74034 to simplify the square root of 74034. 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 74034. The factors of 74034 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 457, 914, 1371, 2742, 4113, 8226, 12339, 24678, 37017, and 74034. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 74034 divided by the greatest perfect square from the list of all factors of 74034. We determined above that the greatest perfect square from the list of all factors of 74034 is 81. Furthermore, 74034 divided by 81 is 914, therefore B equals 914.

Now we have A and B and can get our answer to 74034 in its simplest radical form as follows:

√74034 = A√B

√74034 = 9√914

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74034 to simplify the square root of 74034 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 74034 and then take the square root of that product. The prime factors that multiply together to make 74034 are 2 x 3 x 3 x 3 x 3 x 457. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 74034 by the number (A) squared. 9 squared is 81 and 74034 divided by 81 is 914. Therefore, B equals 914.

Once again we have A and B and can get our answer to 74034 in its simplest radical form as follows:

√74034 = A√B

√74034 = 9√914

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Simplify Square Root of 74035
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