Simplify Square Root of 57722

Here we will show you two methods that you can use to simplify the square root of 57722. In other words, we will show you how to find the square root of 57722 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.

√57722 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57722 to simplify the square root of 57722. 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 57722. The factors of 57722 are 1, 2, 7, 14, 19, 31, 38, 49, 62, 98, 133, 217, 266, 434, 589, 931, 1178, 1519, 1862, 3038, 4123, 8246, 28861, and 57722. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 57722 divided by the greatest perfect square from the list of all factors of 57722. We determined above that the greatest perfect square from the list of all factors of 57722 is 49. Furthermore, 57722 divided by 49 is 1178, therefore B equals 1178.

Now we have A and B and can get our answer to 57722 in its simplest radical form as follows:

√57722 = A√B

√57722 = 7√1178

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57722 to simplify the square root of 57722 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 57722 and then take the square root of that product. The prime factors that multiply together to make 57722 are 2 x 7 x 7 x 19 x 31. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 57722 by the number (A) squared. 7 squared is 49 and 57722 divided by 49 is 1178. Therefore, B equals 1178.

Once again we have A and B and can get our answer to 57722 in its simplest radical form as follows:

√57722 = A√B

√57722 = 7√1178

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Simplify Square Root of 57723
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