Simplify Square Root of 7774

Here we will show you two methods that you can use to simplify the square root of 7774. In other words, we will show you how to find the square root of 7774 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.

√7774 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 7774 to simplify the square root of 7774. 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 7774. The factors of 7774 are 1, 2, 13, 23, 26, 46, 169, 299, 338, 598, 3887, and 7774. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 7774 divided by the greatest perfect square from the list of all factors of 7774. We determined above that the greatest perfect square from the list of all factors of 7774 is 169. Furthermore, 7774 divided by 169 is 46, therefore B equals 46.

Now we have A and B and can get our answer to 7774 in its simplest radical form as follows:

√7774 = A√B

√7774 = 13√46

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 7774 to simplify the square root of 7774 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 7774 and then take the square root of that product. The prime factors that multiply together to make 7774 are 2 x 13 x 13 x 23. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 7774 by the number (A) squared. 13 squared is 169 and 7774 divided by 169 is 46. Therefore, B equals 46.

Once again we have A and B and can get our answer to 7774 in its simplest radical form as follows:

√7774 = A√B

√7774 = 13√46

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Simplify Square Root of 7775
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