Simplify Square Root of 5280

Here we will show you two methods that you can use to simplify the square root of 5280. In other words, we will show you how to find the square root of 5280 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.

√5280 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 5280 to simplify the square root of 5280. 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 5280. The factors of 5280 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640, and 5280. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 5280 divided by the greatest perfect square from the list of all factors of 5280. We determined above that the greatest perfect square from the list of all factors of 5280 is 16. Furthermore, 5280 divided by 16 is 330, therefore B equals 330.

Now we have A and B and can get our answer to 5280 in its simplest radical form as follows:

√5280 = A√B

√5280 = 4√330

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 5280 to simplify the square root of 5280 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 5280 and then take the square root of that product. The prime factors that multiply together to make 5280 are 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11. 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 5280 by the number (A) squared. 4 squared is 16 and 5280 divided by 16 is 330. Therefore, B equals 330.

Once again we have A and B and can get our answer to 5280 in its simplest radical form as follows:

√5280 = A√B

√5280 = 4√330

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