Simplify Square Root of 66424

Here we will show you two methods that you can use to simplify the square root of 66424. In other words, we will show you how to find the square root of 66424 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.

√66424 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66424 to simplify the square root of 66424. 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 66424. The factors of 66424 are 1, 2, 4, 8, 19, 23, 38, 46, 76, 92, 152, 184, 361, 437, 722, 874, 1444, 1748, 2888, 3496, 8303, 16606, 33212, and 66424. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 66424 divided by the greatest perfect square from the list of all factors of 66424. We determined above that the greatest perfect square from the list of all factors of 66424 is 1444. Furthermore, 66424 divided by 1444 is 46, therefore B equals 46.

Now we have A and B and can get our answer to 66424 in its simplest radical form as follows:

√66424 = A√B

√66424 = 38√46

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66424 to simplify the square root of 66424 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 66424 and then take the square root of that product. The prime factors that multiply together to make 66424 are 2 x 2 x 2 x 19 x 19 x 23. When we strip out the pairs only, we get 2 x 2 x 19 x 19 = 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Divide 66424 by the number (A) squared. 38 squared is 1444 and 66424 divided by 1444 is 46. Therefore, B equals 46.

Once again we have A and B and can get our answer to 66424 in its simplest radical form as follows:

√66424 = A√B

√66424 = 38√46

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