Simplify Square Root of 68651

Here we will show you two methods that you can use to simplify the square root of 68651. In other words, we will show you how to find the square root of 68651 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.

√68651 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68651 to simplify the square root of 68651. 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 68651. The factors of 68651 are 1, 11, 79, 869, 6241, and 68651. Furthermore, the greatest perfect square on this list is 6241 and the square root of 6241 is 79. Therefore, A equals 79.

B = Calculate 68651 divided by the greatest perfect square from the list of all factors of 68651. We determined above that the greatest perfect square from the list of all factors of 68651 is 6241. Furthermore, 68651 divided by 6241 is 11, therefore B equals 11.

Now we have A and B and can get our answer to 68651 in its simplest radical form as follows:

√68651 = A√B

√68651 = 79√11

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68651 to simplify the square root of 68651 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 68651 and then take the square root of that product. The prime factors that multiply together to make 68651 are 11 x 79 x 79. When we strip out the pairs only, we get 79 x 79 = 6241 and the square root of 6241 is 79. Therefore, A equals 79.

B = Divide 68651 by the number (A) squared. 79 squared is 6241 and 68651 divided by 6241 is 11. Therefore, B equals 11.

Once again we have A and B and can get our answer to 68651 in its simplest radical form as follows:

√68651 = A√B

√68651 = 79√11

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Simplify Square Root of 68652
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