Simplify Square Root of 68493

Here we will show you two methods that you can use to simplify the square root of 68493. In other words, we will show you how to find the square root of 68493 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.

√68493 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68493 to simplify the square root of 68493. 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 68493. The factors of 68493 are 1, 3, 17, 51, 79, 237, 289, 867, 1343, 4029, 22831, and 68493. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 68493 divided by the greatest perfect square from the list of all factors of 68493. We determined above that the greatest perfect square from the list of all factors of 68493 is 289. Furthermore, 68493 divided by 289 is 237, therefore B equals 237.

Now we have A and B and can get our answer to 68493 in its simplest radical form as follows:

√68493 = A√B

√68493 = 17√237

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68493 to simplify the square root of 68493 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 68493 and then take the square root of that product. The prime factors that multiply together to make 68493 are 3 x 17 x 17 x 79. 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 68493 by the number (A) squared. 17 squared is 289 and 68493 divided by 289 is 237. Therefore, B equals 237.

Once again we have A and B and can get our answer to 68493 in its simplest radical form as follows:

√68493 = A√B

√68493 = 17√237

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Simplify Square Root of 68494
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