Simplify Square Root of 22540

Here we will show you two methods that you can use to simplify the square root of 22540. In other words, we will show you how to find the square root of 22540 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.

√22540 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22540 to simplify the square root of 22540. 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 22540. The factors of 22540 are 1, 2, 4, 5, 7, 10, 14, 20, 23, 28, 35, 46, 49, 70, 92, 98, 115, 140, 161, 196, 230, 245, 322, 460, 490, 644, 805, 980, 1127, 1610, 2254, 3220, 4508, 5635, 11270, and 22540. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 22540 divided by the greatest perfect square from the list of all factors of 22540. We determined above that the greatest perfect square from the list of all factors of 22540 is 196. Furthermore, 22540 divided by 196 is 115, therefore B equals 115.

Now we have A and B and can get our answer to 22540 in its simplest radical form as follows:

√22540 = A√B

√22540 = 14√115

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22540 to simplify the square root of 22540 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 22540 and then take the square root of that product. The prime factors that multiply together to make 22540 are 2 x 2 x 5 x 7 x 7 x 23. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 22540 by the number (A) squared. 14 squared is 196 and 22540 divided by 196 is 115. Therefore, B equals 115.

Once again we have A and B and can get our answer to 22540 in its simplest radical form as follows:

√22540 = A√B

√22540 = 14√115

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