Simplify Square Root of 45760

Here we will show you two methods that you can use to simplify the square root of 45760. In other words, we will show you how to find the square root of 45760 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.

√45760 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 45760 to simplify the square root of 45760. 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 45760. The factors of 45760 are 1, 2, 4, 5, 8, 10, 11, 13, 16, 20, 22, 26, 32, 40, 44, 52, 55, 64, 65, 80, 88, 104, 110, 130, 143, 160, 176, 208, 220, 260, 286, 320, 352, 416, 440, 520, 572, 704, 715, 832, 880, 1040, 1144, 1430, 1760, 2080, 2288, 2860, 3520, 4160, 4576, 5720, 9152, 11440, 22880, and 45760. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 45760 divided by the greatest perfect square from the list of all factors of 45760. We determined above that the greatest perfect square from the list of all factors of 45760 is 64. Furthermore, 45760 divided by 64 is 715, therefore B equals 715.

Now we have A and B and can get our answer to 45760 in its simplest radical form as follows:

√45760 = A√B

√45760 = 8√715

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 45760 to simplify the square root of 45760 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 45760 and then take the square root of that product. The prime factors that multiply together to make 45760 are 2 x 2 x 2 x 2 x 2 x 2 x 5 x 11 x 13. 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 45760 by the number (A) squared. 8 squared is 64 and 45760 divided by 64 is 715. Therefore, B equals 715.

Once again we have A and B and can get our answer to 45760 in its simplest radical form as follows:

√45760 = A√B

√45760 = 8√715

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