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:

\( \sqrt{\frac{81}{16}} \)
\( \frac{\sqrt{81}}{\sqrt{16}} \)
\( \frac{\sqrt{9^2}}{\sqrt{4^2}} \)
\( \frac{9}{4} \)
2\(\frac{1}{4}\)

If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 33 large cakes are needed for the party so \( \frac{33}{4} \) = 8\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 10 x 2 = 20 small cakes during that time. 150 small cakes are needed for the party so \( \frac{150}{20} \) = 7\(\frac{1}{2}\) 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 9 + 8 = 17 cooks.

The equation for this sequence is:

a_n = a_n-1 + 3(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 3(6 - 1)
a₆ = 31 + 3(5)
a₆ = 46

There are 2 2-passenger taxis available so that's 2 x 2 = 4 total seats. There are 7 people needing transportation leaving 7 - 4 = 3 who will have to find other transportation.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.