Simplify Square Root of 29760

Here we will show you two methods that you can use to simplify the square root of 29760. In other words, we will show you how to find the square root of 29760 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.

√29760 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 29760 to simplify the square root of 29760. 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 29760. The factors of 29760 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 155, 160, 186, 192, 240, 248, 310, 320, 372, 465, 480, 496, 620, 744, 930, 960, 992, 1240, 1488, 1860, 1984, 2480, 2976, 3720, 4960, 5952, 7440, 9920, 14880, and 29760. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 29760 divided by the greatest perfect square from the list of all factors of 29760. We determined above that the greatest perfect square from the list of all factors of 29760 is 64. Furthermore, 29760 divided by 64 is 465, therefore B equals 465.

Now we have A and B and can get our answer to 29760 in its simplest radical form as follows:

√29760 = A√B

√29760 = 8√465

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 29760 to simplify the square root of 29760 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 29760 and then take the square root of that product. The prime factors that multiply together to make 29760 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 31. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 29760 by the number (A) squared. 8 squared is 64 and 29760 divided by 64 is 465. Therefore, B equals 465.

Once again we have A and B and can get our answer to 29760 in its simplest radical form as follows:

√29760 = A√B

√29760 = 8√465

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Simplify Square Root of 29761
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