Simplify Square Root of 67276

Here we will show you two methods that you can use to simplify the square root of 67276. In other words, we will show you how to find the square root of 67276 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.

√67276 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 67276 to simplify the square root of 67276. 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 67276. The factors of 67276 are 1, 2, 4, 11, 22, 44, 121, 139, 242, 278, 484, 556, 1529, 3058, 6116, 16819, 33638, and 67276. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 67276 divided by the greatest perfect square from the list of all factors of 67276. We determined above that the greatest perfect square from the list of all factors of 67276 is 484. Furthermore, 67276 divided by 484 is 139, therefore B equals 139.

Now we have A and B and can get our answer to 67276 in its simplest radical form as follows:

√67276 = A√B

√67276 = 22√139

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 67276 to simplify the square root of 67276 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 67276 and then take the square root of that product. The prime factors that multiply together to make 67276 are 2 x 2 x 11 x 11 x 139. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 67276 by the number (A) squared. 22 squared is 484 and 67276 divided by 484 is 139. Therefore, B equals 139.

Once again we have A and B and can get our answer to 67276 in its simplest radical form as follows:

√67276 = A√B

√67276 = 22√139

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Simplify Square Root of 67277
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