Simplify Square Root of 68697

Here we will show you two methods that you can use to simplify the square root of 68697. In other words, we will show you how to find the square root of 68697 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.

√68697 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68697 to simplify the square root of 68697. 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 68697. The factors of 68697 are 1, 3, 9, 17, 51, 153, 449, 1347, 4041, 7633, 22899, and 68697. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 68697 divided by the greatest perfect square from the list of all factors of 68697. We determined above that the greatest perfect square from the list of all factors of 68697 is 9. Furthermore, 68697 divided by 9 is 7633, therefore B equals 7633.

Now we have A and B and can get our answer to 68697 in its simplest radical form as follows:

√68697 = A√B

√68697 = 3√7633

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68697 to simplify the square root of 68697 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 68697 and then take the square root of that product. The prime factors that multiply together to make 68697 are 3 x 3 x 17 x 449. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 68697 by the number (A) squared. 3 squared is 9 and 68697 divided by 9 is 7633. Therefore, B equals 7633.

Once again we have A and B and can get our answer to 68697 in its simplest radical form as follows:

√68697 = A√B

√68697 = 3√7633

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Simplify Square Root of 68698
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