Simplify Square Root of 71040

Here we will show you two methods that you can use to simplify the square root of 71040. In other words, we will show you how to find the square root of 71040 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.

√71040 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 71040 to simplify the square root of 71040. 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 71040. The factors of 71040 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 37, 40, 48, 60, 64, 74, 80, 96, 111, 120, 128, 148, 160, 185, 192, 222, 240, 296, 320, 370, 384, 444, 480, 555, 592, 640, 740, 888, 960, 1110, 1184, 1480, 1776, 1920, 2220, 2368, 2960, 3552, 4440, 4736, 5920, 7104, 8880, 11840, 14208, 17760, 23680, 35520, and 71040. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 71040 divided by the greatest perfect square from the list of all factors of 71040. We determined above that the greatest perfect square from the list of all factors of 71040 is 64. Furthermore, 71040 divided by 64 is 1110, therefore B equals 1110.

Now we have A and B and can get our answer to 71040 in its simplest radical form as follows:

√71040 = A√B

√71040 = 8√1110

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 71040 to simplify the square root of 71040 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 71040 and then take the square root of that product. The prime factors that multiply together to make 71040 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 37. 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 71040 by the number (A) squared. 8 squared is 64 and 71040 divided by 64 is 1110. Therefore, B equals 1110.

Once again we have A and B and can get our answer to 71040 in its simplest radical form as follows:

√71040 = A√B

√71040 = 8√1110

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