Simplify Square Root of 48684

Here we will show you two methods that you can use to simplify the square root of 48684. In other words, we will show you how to find the square root of 48684 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.

√48684 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 48684 to simplify the square root of 48684. 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 48684. The factors of 48684 are 1, 2, 3, 4, 6, 12, 4057, 8114, 12171, 16228, 24342, and 48684. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 48684 divided by the greatest perfect square from the list of all factors of 48684. We determined above that the greatest perfect square from the list of all factors of 48684 is 4. Furthermore, 48684 divided by 4 is 12171, therefore B equals 12171.

Now we have A and B and can get our answer to 48684 in its simplest radical form as follows:

√48684 = A√B

√48684 = 2√12171

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 48684 to simplify the square root of 48684 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 48684 and then take the square root of that product. The prime factors that multiply together to make 48684 are 2 x 2 x 3 x 4057. 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 48684 by the number (A) squared. 2 squared is 4 and 48684 divided by 4 is 12171. Therefore, B equals 12171.

Once again we have A and B and can get our answer to 48684 in its simplest radical form as follows:

√48684 = A√B

√48684 = 2√12171

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Simplify Square Root of 48685
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