Simplify Square Root of 47096

Here we will show you two methods that you can use to simplify the square root of 47096. In other words, we will show you how to find the square root of 47096 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.

√47096 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 47096 to simplify the square root of 47096. 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 47096. The factors of 47096 are 1, 2, 4, 7, 8, 14, 28, 29, 56, 58, 116, 203, 232, 406, 812, 841, 1624, 1682, 3364, 5887, 6728, 11774, 23548, and 47096. Furthermore, the greatest perfect square on this list is 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Calculate 47096 divided by the greatest perfect square from the list of all factors of 47096. We determined above that the greatest perfect square from the list of all factors of 47096 is 3364. Furthermore, 47096 divided by 3364 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 47096 in its simplest radical form as follows:

√47096 = A√B

√47096 = 58√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 47096 to simplify the square root of 47096 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 47096 and then take the square root of that product. The prime factors that multiply together to make 47096 are 2 x 2 x 2 x 7 x 29 x 29. When we strip out the pairs only, we get 2 x 2 x 29 x 29 = 3364 and the square root of 3364 is 58. Therefore, A equals 58.

B = Divide 47096 by the number (A) squared. 58 squared is 3364 and 47096 divided by 3364 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 47096 in its simplest radical form as follows:

√47096 = A√B

√47096 = 58√14

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Simplify Square Root of 47097
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