Simplify Square Root of 4332

Here we will show you two methods that you can use to simplify the square root of 4332. In other words, we will show you how to find the square root of 4332 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.

√4332 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 4332 to simplify the square root of 4332. 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 4332. The factors of 4332 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228, 361, 722, 1083, 1444, 2166, and 4332. Furthermore, the greatest perfect square on this list is 1444 and the square root of 1444 is 38. Therefore, A equals 38.

B = Calculate 4332 divided by the greatest perfect square from the list of all factors of 4332. We determined above that the greatest perfect square from the list of all factors of 4332 is 1444. Furthermore, 4332 divided by 1444 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 4332 in its simplest radical form as follows:

√4332 = A√B

√4332 = 38√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 4332 to simplify the square root of 4332 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 4332 and then take the square root of that product. The prime factors that multiply together to make 4332 are 2 x 2 x 3 x 19 x 19. 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 4332 by the number (A) squared. 38 squared is 1444 and 4332 divided by 1444 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 4332 in its simplest radical form as follows:

√4332 = A√B

√4332 = 38√3

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Simplify Square Root of 4333
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