Simplify Square Root of 71442

Here we will show you two methods that you can use to simplify the square root of 71442. In other words, we will show you how to find the square root of 71442 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.

√71442 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 71442 to simplify the square root of 71442. 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 71442. The factors of 71442 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 49, 54, 63, 81, 98, 126, 147, 162, 189, 243, 294, 378, 441, 486, 567, 729, 882, 1134, 1323, 1458, 1701, 2646, 3402, 3969, 5103, 7938, 10206, 11907, 23814, 35721, and 71442. Furthermore, the greatest perfect square on this list is 35721 and the square root of 35721 is 189. Therefore, A equals 189.

B = Calculate 71442 divided by the greatest perfect square from the list of all factors of 71442. We determined above that the greatest perfect square from the list of all factors of 71442 is 35721. Furthermore, 71442 divided by 35721 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 71442 in its simplest radical form as follows:

√71442 = A√B

√71442 = 189√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 71442 to simplify the square root of 71442 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 71442 and then take the square root of that product. The prime factors that multiply together to make 71442 are 2 x 3 x 3 x 3 x 3 x 3 x 3 x 7 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 3 x 3 x 7 x 7 = 35721 and the square root of 35721 is 189. Therefore, A equals 189.

B = Divide 71442 by the number (A) squared. 189 squared is 35721 and 71442 divided by 35721 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 71442 in its simplest radical form as follows:

√71442 = A√B

√71442 = 189√2

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