Simplify Square Root of 73117

Here we will show you two methods that you can use to simplify the square root of 73117. In other words, we will show you how to find the square root of 73117 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.

√73117 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 73117 to simplify the square root of 73117. 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 73117. The factors of 73117 are 1, 11, 17, 23, 187, 253, 289, 391, 3179, 4301, 6647, and 73117. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 73117 divided by the greatest perfect square from the list of all factors of 73117. We determined above that the greatest perfect square from the list of all factors of 73117 is 289. Furthermore, 73117 divided by 289 is 253, therefore B equals 253.

Now we have A and B and can get our answer to 73117 in its simplest radical form as follows:

√73117 = A√B

√73117 = 17√253

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 73117 to simplify the square root of 73117 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 73117 and then take the square root of that product. The prime factors that multiply together to make 73117 are 11 x 17 x 17 x 23. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 73117 by the number (A) squared. 17 squared is 289 and 73117 divided by 289 is 253. Therefore, B equals 253.

Once again we have A and B and can get our answer to 73117 in its simplest radical form as follows:

√73117 = A√B

√73117 = 17√253

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Simplify Square Root of 73118
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