Simplify Square Root of 47432

Here we will show you two methods that you can use to simplify the square root of 47432. In other words, we will show you how to find the square root of 47432 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.

√47432 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 47432 to simplify the square root of 47432. 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 47432. The factors of 47432 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 49, 56, 77, 88, 98, 121, 154, 196, 242, 308, 392, 484, 539, 616, 847, 968, 1078, 1694, 2156, 3388, 4312, 5929, 6776, 11858, 23716, and 47432. Furthermore, the greatest perfect square on this list is 23716 and the square root of 23716 is 154. Therefore, A equals 154.

B = Calculate 47432 divided by the greatest perfect square from the list of all factors of 47432. We determined above that the greatest perfect square from the list of all factors of 47432 is 23716. Furthermore, 47432 divided by 23716 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 47432 in its simplest radical form as follows:

√47432 = A√B

√47432 = 154√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 47432 to simplify the square root of 47432 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 47432 and then take the square root of that product. The prime factors that multiply together to make 47432 are 2 x 2 x 2 x 7 x 7 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 7 x 7 x 11 x 11 = 23716 and the square root of 23716 is 154. Therefore, A equals 154.

B = Divide 47432 by the number (A) squared. 154 squared is 23716 and 47432 divided by 23716 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 47432 in its simplest radical form as follows:

√47432 = A√B

√47432 = 154√2

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