Simplify Square Root of 7488

Here we will show you two methods that you can use to simplify the square root of 7488. In other words, we will show you how to find the square root of 7488 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.

√7488 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7488 to simplify the square root of 7488. 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 7488. The factors of 7488 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 64, 72, 78, 96, 104, 117, 144, 156, 192, 208, 234, 288, 312, 416, 468, 576, 624, 832, 936, 1248, 1872, 2496, 3744, and 7488. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 7488 divided by the greatest perfect square from the list of all factors of 7488. We determined above that the greatest perfect square from the list of all factors of 7488 is 576. Furthermore, 7488 divided by 576 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 7488 in its simplest radical form as follows:

√7488 = A√B

√7488 = 24√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7488 to simplify the square root of 7488 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 7488 and then take the square root of that product. The prime factors that multiply together to make 7488 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 7488 by the number (A) squared. 24 squared is 576 and 7488 divided by 576 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 7488 in its simplest radical form as follows:

√7488 = A√B

√7488 = 24√13

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