Simplify Square Root of 51768

Here we will show you two methods that you can use to simplify the square root of 51768. In other words, we will show you how to find the square root of 51768 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.

√51768 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 51768 to simplify the square root of 51768. 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 51768. The factors of 51768 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 719, 1438, 2157, 2876, 4314, 5752, 6471, 8628, 12942, 17256, 25884, and 51768. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 51768 divided by the greatest perfect square from the list of all factors of 51768. We determined above that the greatest perfect square from the list of all factors of 51768 is 36. Furthermore, 51768 divided by 36 is 1438, therefore B equals 1438.

Now we have A and B and can get our answer to 51768 in its simplest radical form as follows:

√51768 = A√B

√51768 = 6√1438

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 51768 to simplify the square root of 51768 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 51768 and then take the square root of that product. The prime factors that multiply together to make 51768 are 2 x 2 x 2 x 3 x 3 x 719. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 51768 by the number (A) squared. 6 squared is 36 and 51768 divided by 36 is 1438. Therefore, B equals 1438.

Once again we have A and B and can get our answer to 51768 in its simplest radical form as follows:

√51768 = A√B

√51768 = 6√1438

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Simplify Square Root of 51769
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