Simplify Square Root of 726

Here we will show you two methods that you can use to simplify the square root of 726. In other words, we will show you how to find the square root of 726 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.

√726 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 726 to simplify the square root of 726. 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 726. The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 726 divided by the greatest perfect square from the list of all factors of 726. We determined above that the greatest perfect square from the list of all factors of 726 is 121. Furthermore, 726 divided by 121 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 726 in its simplest radical form as follows:

√726 = A√B

√726 = 11√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 726 to simplify the square root of 726 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 726 and then take the square root of that product. The prime factors that multiply together to make 726 are 2 x 3 x 11 x 11. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 726 by the number (A) squared. 11 squared is 121 and 726 divided by 121 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 726 in its simplest radical form as follows:

√726 = A√B

√726 = 11√6

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Simplify Square Root of 727
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