Simplify Square Root of 22734

Here we will show you two methods that you can use to simplify the square root of 22734. In other words, we will show you how to find the square root of 22734 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.

√22734 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22734 to simplify the square root of 22734. 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 22734. The factors of 22734 are 1, 2, 3, 6, 9, 18, 27, 54, 421, 842, 1263, 2526, 3789, 7578, 11367, and 22734. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 22734 divided by the greatest perfect square from the list of all factors of 22734. We determined above that the greatest perfect square from the list of all factors of 22734 is 9. Furthermore, 22734 divided by 9 is 2526, therefore B equals 2526.

Now we have A and B and can get our answer to 22734 in its simplest radical form as follows:

√22734 = A√B

√22734 = 3√2526

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22734 to simplify the square root of 22734 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 22734 and then take the square root of that product. The prime factors that multiply together to make 22734 are 2 x 3 x 3 x 3 x 421. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 22734 by the number (A) squared. 3 squared is 9 and 22734 divided by 9 is 2526. Therefore, B equals 2526.

Once again we have A and B and can get our answer to 22734 in its simplest radical form as follows:

√22734 = A√B

√22734 = 3√2526

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Simplify Square Root of 22735
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