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:

\( \sqrt{\frac{25}{81}} \)
\( \frac{\sqrt{25}}{\sqrt{81}} \)
\( \frac{\sqrt{5^2}}{\sqrt{9^2}} \)
\(\frac{5}{9}\)

A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

37,000 fans x \( \frac{4}{5} \) = \( \frac{148000}{5} \) = 29,600 fans.

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{5} \) ÷ \( \frac{4}{9} \) = \( \frac{3}{5} \) x \( \frac{9}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{5} \) x \( \frac{9}{4} \) = \( \frac{3 x 9}{5 x 4} \) = \( \frac{27}{20} \) = 1\(\frac{7}{20}\)

To simplify a radical, factor out the perfect squares:

\( \sqrt{20} \)
\( \sqrt{4 \times 5} \)
\( \sqrt{2^2 \times 5} \)
2\( \sqrt{5} \)

To add these radicals together their radicands must be the same:

9\( \sqrt{18} \) + 7\( \sqrt{2} \)
9\( \sqrt{9 \times 2} \) + 7\( \sqrt{2} \)
9\( \sqrt{3^2 \times 2} \) + 7\( \sqrt{2} \)
(9)(3)\( \sqrt{2} \) + 7\( \sqrt{2} \)
27\( \sqrt{2} \) + 7\( \sqrt{2} \)

Now that the radicands are identical, you can add them together: