Simplify Square Root of 783

Here we will show you two methods that you can use to simplify the square root of 783. In other words, we will show you how to find the square root of 783 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.

√783 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 783 to simplify the square root of 783. 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 783. The factors of 783 are 1, 3, 9, 27, 29, 87, 261, and 783. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 783 divided by the greatest perfect square from the list of all factors of 783. We determined above that the greatest perfect square from the list of all factors of 783 is 9. Furthermore, 783 divided by 9 is 87, therefore B equals 87.

Now we have A and B and can get our answer to 783 in its simplest radical form as follows:

√783 = A√B

√783 = 3√87

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 783 to simplify the square root of 783 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 783 and then take the square root of that product. The prime factors that multiply together to make 783 are 3 x 3 x 3 x 29. 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 783 by the number (A) squared. 3 squared is 9 and 783 divided by 9 is 87. Therefore, B equals 87.

Once again we have A and B and can get our answer to 783 in its simplest radical form as follows:

√783 = A√B

√783 = 3√87

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Simplify Square Root of 784
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