Simplify Square Root of 14760

Here we will show you two methods that you can use to simplify the square root of 14760. In other words, we will show you how to find the square root of 14760 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.

√14760 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 14760 to simplify the square root of 14760. 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 14760. The factors of 14760 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 41, 45, 60, 72, 82, 90, 120, 123, 164, 180, 205, 246, 328, 360, 369, 410, 492, 615, 738, 820, 984, 1230, 1476, 1640, 1845, 2460, 2952, 3690, 4920, 7380, and 14760. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 14760 divided by the greatest perfect square from the list of all factors of 14760. We determined above that the greatest perfect square from the list of all factors of 14760 is 36. Furthermore, 14760 divided by 36 is 410, therefore B equals 410.

Now we have A and B and can get our answer to 14760 in its simplest radical form as follows:

√14760 = A√B

√14760 = 6√410

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 14760 to simplify the square root of 14760 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 14760 and then take the square root of that product. The prime factors that multiply together to make 14760 are 2 x 2 x 2 x 3 x 3 x 5 x 41. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 14760 by the number (A) squared. 6 squared is 36 and 14760 divided by 36 is 410. Therefore, B equals 410.

Once again we have A and B and can get our answer to 14760 in its simplest radical form as follows:

√14760 = A√B

√14760 = 6√410

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