Simplify Square Root of 49329

Here we will show you two methods that you can use to simplify the square root of 49329. In other words, we will show you how to find the square root of 49329 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.

√49329 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49329 to simplify the square root of 49329. 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 49329. The factors of 49329 are 1, 3, 7, 9, 21, 27, 29, 63, 81, 87, 189, 203, 243, 261, 567, 609, 783, 1701, 1827, 2349, 5481, 7047, 16443, and 49329. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 49329 divided by the greatest perfect square from the list of all factors of 49329. We determined above that the greatest perfect square from the list of all factors of 49329 is 81. Furthermore, 49329 divided by 81 is 609, therefore B equals 609.

Now we have A and B and can get our answer to 49329 in its simplest radical form as follows:

√49329 = A√B

√49329 = 9√609

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49329 to simplify the square root of 49329 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 49329 and then take the square root of that product. The prime factors that multiply together to make 49329 are 3 x 3 x 3 x 3 x 3 x 7 x 29. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 49329 by the number (A) squared. 9 squared is 81 and 49329 divided by 81 is 609. Therefore, B equals 609.

Once again we have A and B and can get our answer to 49329 in its simplest radical form as follows:

√49329 = A√B

√49329 = 9√609

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