Simplify Square Root of 29680

Here we will show you two methods that you can use to simplify the square root of 29680. In other words, we will show you how to find the square root of 29680 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.

√29680 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 29680 to simplify the square root of 29680. 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 29680. The factors of 29680 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 53, 56, 70, 80, 106, 112, 140, 212, 265, 280, 371, 424, 530, 560, 742, 848, 1060, 1484, 1855, 2120, 2968, 3710, 4240, 5936, 7420, 14840, and 29680. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 29680 divided by the greatest perfect square from the list of all factors of 29680. We determined above that the greatest perfect square from the list of all factors of 29680 is 16. Furthermore, 29680 divided by 16 is 1855, therefore B equals 1855.

Now we have A and B and can get our answer to 29680 in its simplest radical form as follows:

√29680 = A√B

√29680 = 4√1855

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 29680 to simplify the square root of 29680 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 29680 and then take the square root of that product. The prime factors that multiply together to make 29680 are 2 x 2 x 2 x 2 x 5 x 7 x 53. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 29680 by the number (A) squared. 4 squared is 16 and 29680 divided by 16 is 1855. Therefore, B equals 1855.

Once again we have A and B and can get our answer to 29680 in its simplest radical form as follows:

√29680 = A√B

√29680 = 4√1855

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