Simplify Square Root of 68607

Here we will show you two methods that you can use to simplify the square root of 68607. In other words, we will show you how to find the square root of 68607 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.

√68607 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68607 to simplify the square root of 68607. 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 68607. The factors of 68607 are 1, 3, 7, 9, 11, 21, 27, 33, 63, 77, 81, 99, 121, 189, 231, 297, 363, 567, 693, 847, 891, 1089, 2079, 2541, 3267, 6237, 7623, 9801, 22869, and 68607. Furthermore, the greatest perfect square on this list is 9801 and the square root of 9801 is 99. Therefore, A equals 99.

B = Calculate 68607 divided by the greatest perfect square from the list of all factors of 68607. We determined above that the greatest perfect square from the list of all factors of 68607 is 9801. Furthermore, 68607 divided by 9801 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 68607 in its simplest radical form as follows:

√68607 = A√B

√68607 = 99√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68607 to simplify the square root of 68607 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 68607 and then take the square root of that product. The prime factors that multiply together to make 68607 are 3 x 3 x 3 x 3 x 7 x 11 x 11. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 11 x 11 = 9801 and the square root of 9801 is 99. Therefore, A equals 99.

B = Divide 68607 by the number (A) squared. 99 squared is 9801 and 68607 divided by 9801 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 68607 in its simplest radical form as follows:

√68607 = A√B

√68607 = 99√7

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