A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

The greatest common factor (GCF) is the greatest factor that divides two integers.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (3 + 4) ÷ 3 x 4 - 4²
P: 2 + (7) ÷ 3 x 4 - 4²
E: 2 + 7 ÷ 3 x 4 - 16
MD: 2 + \( \frac{7}{3} \) x 4 - 16
MD: 2 + \( \frac{28}{3} \) - 16
AS: \( \frac{6}{3} \) + \( \frac{28}{3} \) - 16
AS: \( \frac{34}{3} \) - 16
AS: \( \frac{34 - 48}{3} \)
\( \frac{-14}{3} \)
-4\(\frac{2}{3}\)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{4}{36}} \)
\( \frac{\sqrt{4}}{\sqrt{36}} \)
\( \frac{\sqrt{2^2}}{\sqrt{6^2}} \)
\(\frac{1}{3}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{8 x 3}{2 x 3} \) - \( \frac{3 x 1}{6 x 1} \)

\( \frac{24}{6} \) - \( \frac{3}{6} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{24 - 3}{6} \) = \( \frac{21}{6} \) = 3\(\frac{1}{2}\)