Simplify Square Root of 774

Here we will show you two methods that you can use to simplify the square root of 774. In other words, we will show you how to find the square root of 774 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.

√774 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 774 to simplify the square root of 774. 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 774. The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, and 774. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 774 divided by the greatest perfect square from the list of all factors of 774. We determined above that the greatest perfect square from the list of all factors of 774 is 9. Furthermore, 774 divided by 9 is 86, therefore B equals 86.

Now we have A and B and can get our answer to 774 in its simplest radical form as follows:

√774 = A√B

√774 = 3√86

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 774 to simplify the square root of 774 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 774 and then take the square root of that product. The prime factors that multiply together to make 774 are 2 x 3 x 3 x 43. 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 774 by the number (A) squared. 3 squared is 9 and 774 divided by 9 is 86. Therefore, B equals 86.

Once again we have A and B and can get our answer to 774 in its simplest radical form as follows:

√774 = A√B

√774 = 3√86

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Simplify Square Root of 775
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