Simplify Square Root of 4824

Here we will show you two methods that you can use to simplify the square root of 4824. In other words, we will show you how to find the square root of 4824 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.

√4824 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 4824 to simplify the square root of 4824. 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 4824. The factors of 4824 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 67, 72, 134, 201, 268, 402, 536, 603, 804, 1206, 1608, 2412, and 4824. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 4824 divided by the greatest perfect square from the list of all factors of 4824. We determined above that the greatest perfect square from the list of all factors of 4824 is 36. Furthermore, 4824 divided by 36 is 134, therefore B equals 134.

Now we have A and B and can get our answer to 4824 in its simplest radical form as follows:

√4824 = A√B

√4824 = 6√134

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 4824 to simplify the square root of 4824 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 4824 and then take the square root of that product. The prime factors that multiply together to make 4824 are 2 x 2 x 2 x 3 x 3 x 67. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 4824 by the number (A) squared. 6 squared is 36 and 4824 divided by 36 is 134. Therefore, B equals 134.

Once again we have A and B and can get our answer to 4824 in its simplest radical form as follows:

√4824 = A√B

√4824 = 6√134

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Simplify Square Root of 4825
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