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:

\( \sqrt{\frac{4}{9}} \)
\( \frac{\sqrt{4}}{\sqrt{9}} \)
\( \frac{\sqrt{2^2}}{\sqrt{3^2}} \)
\(\frac{2}{3}\)

To simplify a radical, factor out the perfect squares:

\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)

A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

46,000 fans x \( \frac{5}{6} \) = \( \frac{230000}{6} \) = 38,333 fans.

If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 30 large cakes are needed for the party so \( \frac{30}{6} \) = 5 cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 13 x 2 = 26 small cakes during that time. 360 small cakes are needed for the party so \( \frac{360}{26} \) = 13\(\frac{11}{13}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 5 + 14 = 19 cooks.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).