Simplify Square Root of 68890

Here we will show you two methods that you can use to simplify the square root of 68890. In other words, we will show you how to find the square root of 68890 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.

√68890 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68890 to simplify the square root of 68890. 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 68890. The factors of 68890 are 1, 2, 5, 10, 83, 166, 415, 830, 6889, 13778, 34445, and 68890. Furthermore, the greatest perfect square on this list is 6889 and the square root of 6889 is 83. Therefore, A equals 83.

B = Calculate 68890 divided by the greatest perfect square from the list of all factors of 68890. We determined above that the greatest perfect square from the list of all factors of 68890 is 6889. Furthermore, 68890 divided by 6889 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 68890 in its simplest radical form as follows:

√68890 = A√B

√68890 = 83√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68890 to simplify the square root of 68890 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 68890 and then take the square root of that product. The prime factors that multiply together to make 68890 are 2 x 5 x 83 x 83. When we strip out the pairs only, we get 83 x 83 = 6889 and the square root of 6889 is 83. Therefore, A equals 83.

B = Divide 68890 by the number (A) squared. 83 squared is 6889 and 68890 divided by 6889 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 68890 in its simplest radical form as follows:

√68890 = A√B

√68890 = 83√10

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Simplify Square Root of 68891
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