Simplify Square Root of 73034

Here we will show you two methods that you can use to simplify the square root of 73034. In other words, we will show you how to find the square root of 73034 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.

√73034 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73034 to simplify the square root of 73034. 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 73034. The factors of 73034 are 1, 2, 13, 26, 53, 106, 689, 1378, 2809, 5618, 36517, and 73034. Furthermore, the greatest perfect square on this list is 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Calculate 73034 divided by the greatest perfect square from the list of all factors of 73034. We determined above that the greatest perfect square from the list of all factors of 73034 is 2809. Furthermore, 73034 divided by 2809 is 26, therefore B equals 26.

Now we have A and B and can get our answer to 73034 in its simplest radical form as follows:

√73034 = A√B

√73034 = 53√26

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73034 to simplify the square root of 73034 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 73034 and then take the square root of that product. The prime factors that multiply together to make 73034 are 2 x 13 x 53 x 53. When we strip out the pairs only, we get 53 x 53 = 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Divide 73034 by the number (A) squared. 53 squared is 2809 and 73034 divided by 2809 is 26. Therefore, B equals 26.

Once again we have A and B and can get our answer to 73034 in its simplest radical form as follows:

√73034 = A√B

√73034 = 53√26

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Simplify Square Root of 73035
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