Simplify Square Root of 56781

Here we will show you two methods that you can use to simplify the square root of 56781. In other words, we will show you how to find the square root of 56781 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.

√56781 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 56781 to simplify the square root of 56781. 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 56781. The factors of 56781 are 1, 3, 9, 27, 81, 701, 2103, 6309, 18927, and 56781. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 56781 divided by the greatest perfect square from the list of all factors of 56781. We determined above that the greatest perfect square from the list of all factors of 56781 is 81. Furthermore, 56781 divided by 81 is 701, therefore B equals 701.

Now we have A and B and can get our answer to 56781 in its simplest radical form as follows:

√56781 = A√B

√56781 = 9√701

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 56781 to simplify the square root of 56781 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 56781 and then take the square root of that product. The prime factors that multiply together to make 56781 are 3 x 3 x 3 x 3 x 701. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 56781 by the number (A) squared. 9 squared is 81 and 56781 divided by 81 is 701. Therefore, B equals 701.

Once again we have A and B and can get our answer to 56781 in its simplest radical form as follows:

√56781 = A√B

√56781 = 9√701

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Simplify Square Root of 56782
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