Simplify Square Root of 30968

Here we will show you two methods that you can use to simplify the square root of 30968. In other words, we will show you how to find the square root of 30968 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.

√30968 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30968 to simplify the square root of 30968. 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 30968. The factors of 30968 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 79, 98, 158, 196, 316, 392, 553, 632, 1106, 2212, 3871, 4424, 7742, 15484, and 30968. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 30968 divided by the greatest perfect square from the list of all factors of 30968. We determined above that the greatest perfect square from the list of all factors of 30968 is 196. Furthermore, 30968 divided by 196 is 158, therefore B equals 158.

Now we have A and B and can get our answer to 30968 in its simplest radical form as follows:

√30968 = A√B

√30968 = 14√158

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30968 to simplify the square root of 30968 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 30968 and then take the square root of that product. The prime factors that multiply together to make 30968 are 2 x 2 x 2 x 7 x 7 x 79. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 30968 by the number (A) squared. 14 squared is 196 and 30968 divided by 196 is 158. Therefore, B equals 158.

Once again we have A and B and can get our answer to 30968 in its simplest radical form as follows:

√30968 = A√B

√30968 = 14√158

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Simplify Square Root of 30969
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