Simplify Square Root of 47716

Here we will show you two methods that you can use to simplify the square root of 47716. In other words, we will show you how to find the square root of 47716 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.

√47716 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 47716 to simplify the square root of 47716. 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 47716. The factors of 47716 are 1, 2, 4, 79, 151, 158, 302, 316, 604, 11929, 23858, and 47716. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 47716 divided by the greatest perfect square from the list of all factors of 47716. We determined above that the greatest perfect square from the list of all factors of 47716 is 4. Furthermore, 47716 divided by 4 is 11929, therefore B equals 11929.

Now we have A and B and can get our answer to 47716 in its simplest radical form as follows:

√47716 = A√B

√47716 = 2√11929

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 47716 to simplify the square root of 47716 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 47716 and then take the square root of that product. The prime factors that multiply together to make 47716 are 2 x 2 x 79 x 151. 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 47716 by the number (A) squared. 2 squared is 4 and 47716 divided by 4 is 11929. Therefore, B equals 11929.

Once again we have A and B and can get our answer to 47716 in its simplest radical form as follows:

√47716 = A√B

√47716 = 2√11929

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Simplify Square Root of 47717
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