Simplify Square Root of 30528

Here we will show you two methods that you can use to simplify the square root of 30528. In other words, we will show you how to find the square root of 30528 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.

√30528 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30528 to simplify the square root of 30528. 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 30528. The factors of 30528 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 53, 64, 72, 96, 106, 144, 159, 192, 212, 288, 318, 424, 477, 576, 636, 848, 954, 1272, 1696, 1908, 2544, 3392, 3816, 5088, 7632, 10176, 15264, and 30528. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 30528 divided by the greatest perfect square from the list of all factors of 30528. We determined above that the greatest perfect square from the list of all factors of 30528 is 576. Furthermore, 30528 divided by 576 is 53, therefore B equals 53.

Now we have A and B and can get our answer to 30528 in its simplest radical form as follows:

√30528 = A√B

√30528 = 24√53

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30528 to simplify the square root of 30528 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 30528 and then take the square root of that product. The prime factors that multiply together to make 30528 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 53. 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 30528 by the number (A) squared. 24 squared is 576 and 30528 divided by 576 is 53. Therefore, B equals 53.

Once again we have A and B and can get our answer to 30528 in its simplest radical form as follows:

√30528 = A√B

√30528 = 24√53

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Simplify Square Root of 30529
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