Simplify Square Root of 2763

Here we will show you two methods that you can use to simplify the square root of 2763. In other words, we will show you how to find the square root of 2763 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.

√2763 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2763 to simplify the square root of 2763. 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 2763. The factors of 2763 are 1, 3, 9, 307, 921, and 2763. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 2763 divided by the greatest perfect square from the list of all factors of 2763. We determined above that the greatest perfect square from the list of all factors of 2763 is 9. Furthermore, 2763 divided by 9 is 307, therefore B equals 307.

Now we have A and B and can get our answer to 2763 in its simplest radical form as follows:

√2763 = A√B

√2763 = 3√307

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2763 to simplify the square root of 2763 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 2763 and then take the square root of that product. The prime factors that multiply together to make 2763 are 3 x 3 x 307. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 2763 by the number (A) squared. 3 squared is 9 and 2763 divided by 9 is 307. Therefore, B equals 307.

Once again we have A and B and can get our answer to 2763 in its simplest radical form as follows:

√2763 = A√B

√2763 = 3√307

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Simplify Square Root of 2764
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