Simplify Square Root of 72729

Here we will show you two methods that you can use to simplify the square root of 72729. In other words, we will show you how to find the square root of 72729 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.

√72729 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72729 to simplify the square root of 72729. 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 72729. The factors of 72729 are 1, 3, 9, 8081, 24243, and 72729. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 72729 divided by the greatest perfect square from the list of all factors of 72729. We determined above that the greatest perfect square from the list of all factors of 72729 is 9. Furthermore, 72729 divided by 9 is 8081, therefore B equals 8081.

Now we have A and B and can get our answer to 72729 in its simplest radical form as follows:

√72729 = A√B

√72729 = 3√8081

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72729 to simplify the square root of 72729 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 72729 and then take the square root of that product. The prime factors that multiply together to make 72729 are 3 x 3 x 8081. 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 72729 by the number (A) squared. 3 squared is 9 and 72729 divided by 9 is 8081. Therefore, B equals 8081.

Once again we have A and B and can get our answer to 72729 in its simplest radical form as follows:

√72729 = A√B

√72729 = 3√8081

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Simplify Square Root of 72730
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