Simplify Square Root of 30424

Here we will show you two methods that you can use to simplify the square root of 30424. In other words, we will show you how to find the square root of 30424 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.

√30424 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 30424 to simplify the square root of 30424. 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 30424. The factors of 30424 are 1, 2, 4, 8, 3803, 7606, 15212, and 30424. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 30424 divided by the greatest perfect square from the list of all factors of 30424. We determined above that the greatest perfect square from the list of all factors of 30424 is 4. Furthermore, 30424 divided by 4 is 7606, therefore B equals 7606.

Now we have A and B and can get our answer to 30424 in its simplest radical form as follows:

√30424 = A√B

√30424 = 2√7606

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 30424 to simplify the square root of 30424 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 30424 and then take the square root of that product. The prime factors that multiply together to make 30424 are 2 x 2 x 2 x 3803. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 30424 by the number (A) squared. 2 squared is 4 and 30424 divided by 4 is 7606. Therefore, B equals 7606.

Once again we have A and B and can get our answer to 30424 in its simplest radical form as follows:

√30424 = A√B

√30424 = 2√7606

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