Simplify Square Root of 30492

Here we will show you two methods that you can use to simplify the square root of 30492. In other words, we will show you how to find the square root of 30492 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.

√30492 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30492 to simplify the square root of 30492. 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 30492. The factors of 30492 are 1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 28, 33, 36, 42, 44, 63, 66, 77, 84, 99, 121, 126, 132, 154, 198, 231, 242, 252, 308, 363, 396, 462, 484, 693, 726, 847, 924, 1089, 1386, 1452, 1694, 2178, 2541, 2772, 3388, 4356, 5082, 7623, 10164, 15246, and 30492. Furthermore, the greatest perfect square on this list is 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Calculate 30492 divided by the greatest perfect square from the list of all factors of 30492. We determined above that the greatest perfect square from the list of all factors of 30492 is 4356. Furthermore, 30492 divided by 4356 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 30492 in its simplest radical form as follows:

√30492 = A√B

√30492 = 66√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30492 to simplify the square root of 30492 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 30492 and then take the square root of that product. The prime factors that multiply together to make 30492 are 2 x 2 x 3 x 3 x 7 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 11 x 11 = 4356 and the square root of 4356 is 66. Therefore, A equals 66.

B = Divide 30492 by the number (A) squared. 66 squared is 4356 and 30492 divided by 4356 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 30492 in its simplest radical form as follows:

√30492 = A√B

√30492 = 66√7

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