To simplify a radical, factor out the perfect squares:

\( \sqrt{45} \)
\( \sqrt{9 \times 5} \)
\( \sqrt{3^2 \times 5} \)
3\( \sqrt{5} \)

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

4 + (2 + 2) ÷ 3 x 4 - 3²
P: 4 + (4) ÷ 3 x 4 - 3²
E: 4 + 4 ÷ 3 x 4 - 9
MD: 4 + \( \frac{4}{3} \) x 4 - 9
MD: 4 + \( \frac{16}{3} \) - 9
AS: \( \frac{12}{3} \) + \( \frac{16}{3} \) - 9
AS: \( \frac{28}{3} \) - 9
AS: \( \frac{28 - 27}{3} \)
\( \frac{1}{3} \)
\(\frac{1}{3}\)

You have 9 out of the total of 100 raffle tickets sold so you have a (\( \frac{9}{100} \)) x 100 = \( \frac{9 \times 100}{100} \) = \( \frac{900}{100} \) = 9% chance to win the raffle.

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:

\( \sqrt{\frac{64}{16}} \)
\( \frac{\sqrt{64}}{\sqrt{16}} \)
\( \frac{\sqrt{8^2}}{\sqrt{4^2}} \)
\( \frac{8}{4} \)
2

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 have in common.