Simplify Square Root of 22842

Here we will show you two methods that you can use to simplify the square root of 22842. In other words, we will show you how to find the square root of 22842 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.

√22842 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22842 to simplify the square root of 22842. 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 22842. The factors of 22842 are 1, 2, 3, 6, 9, 18, 27, 47, 54, 81, 94, 141, 162, 243, 282, 423, 486, 846, 1269, 2538, 3807, 7614, 11421, and 22842. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 22842 divided by the greatest perfect square from the list of all factors of 22842. We determined above that the greatest perfect square from the list of all factors of 22842 is 81. Furthermore, 22842 divided by 81 is 282, therefore B equals 282.

Now we have A and B and can get our answer to 22842 in its simplest radical form as follows:

√22842 = A√B

√22842 = 9√282

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22842 to simplify the square root of 22842 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 22842 and then take the square root of that product. The prime factors that multiply together to make 22842 are 2 x 3 x 3 x 3 x 3 x 3 x 47. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 22842 by the number (A) squared. 9 squared is 81 and 22842 divided by 81 is 282. Therefore, B equals 282.

Once again we have A and B and can get our answer to 22842 in its simplest radical form as follows:

√22842 = A√B

√22842 = 9√282

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Simplify Square Root of 22843
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