Simplify Square Root of 71736

Here we will show you two methods that you can use to simplify the square root of 71736. In other words, we will show you how to find the square root of 71736 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.

√71736 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 71736 to simplify the square root of 71736. 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 71736. The factors of 71736 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 61, 84, 98, 122, 147, 168, 183, 196, 244, 294, 366, 392, 427, 488, 588, 732, 854, 1176, 1281, 1464, 1708, 2562, 2989, 3416, 5124, 5978, 8967, 10248, 11956, 17934, 23912, 35868, and 71736. Furthermore, the greatest perfect square on this list is 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Calculate 71736 divided by the greatest perfect square from the list of all factors of 71736. We determined above that the greatest perfect square from the list of all factors of 71736 is 196. Furthermore, 71736 divided by 196 is 366, therefore B equals 366.

Now we have A and B and can get our answer to 71736 in its simplest radical form as follows:

√71736 = A√B

√71736 = 14√366

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 71736 to simplify the square root of 71736 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 71736 and then take the square root of that product. The prime factors that multiply together to make 71736 are 2 x 2 x 2 x 3 x 7 x 7 x 61. When we strip out the pairs only, we get 2 x 2 x 7 x 7 = 196 and the square root of 196 is 14. Therefore, A equals 14.

B = Divide 71736 by the number (A) squared. 14 squared is 196 and 71736 divided by 196 is 366. Therefore, B equals 366.

Once again we have A and B and can get our answer to 71736 in its simplest radical form as follows:

√71736 = A√B

√71736 = 14√366

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