Simplify Square Root of 68241

Here we will show you two methods that you can use to simplify the square root of 68241. In other words, we will show you how to find the square root of 68241 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.

√68241 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68241 to simplify the square root of 68241. 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 68241. The factors of 68241 are 1, 3, 23, 43, 69, 129, 529, 989, 1587, 2967, 22747, and 68241. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 68241 divided by the greatest perfect square from the list of all factors of 68241. We determined above that the greatest perfect square from the list of all factors of 68241 is 529. Furthermore, 68241 divided by 529 is 129, therefore B equals 129.

Now we have A and B and can get our answer to 68241 in its simplest radical form as follows:

√68241 = A√B

√68241 = 23√129

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68241 to simplify the square root of 68241 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 68241 and then take the square root of that product. The prime factors that multiply together to make 68241 are 3 x 23 x 23 x 43. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 68241 by the number (A) squared. 23 squared is 529 and 68241 divided by 529 is 129. Therefore, B equals 129.

Once again we have A and B and can get our answer to 68241 in its simplest radical form as follows:

√68241 = A√B

√68241 = 23√129

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Simplify Square Root of 68242
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