Random Puzzles 

Workings

Hint
Try finding the cube root of 190,747.

Answer
53, 59, and 61.

Reasoning
Start by taking the cube root of 190,747, which is approximately 57.56.

The next highest prime number is 59:

   190,747 ÷ 59 = 3,233

Let's try the next prime number, which is 61:

     3,233 ÷ 61 = 53

53, 59, and 61, are all prime, and are consecutive, so this is the answer.

Double-Checking
   53 x 59 x 61 = 190,747

Workings

Hint
3 raised to the 5^th power is 3 x 3 x 3 x 3 x 3.

Answer
3 raised to 5^th power.

Reasoning
3 raised to the 5^th power = 3 ^ 5 = 3 x 3 x 3 x 3 x 3 = 243

and

5 raised to the 3^rd power = 5 ^ 3 = 5 x 5 x 5 = 125.

Workings

Hints
taper = p… (10 letters) heals = s… (9 letters) brows = b… (7 letters) often = f… (8 letters) farce = c… (8 letters) yowls = s… (6 letters) satin = a… (10 letters) awful = l… (6 letters) iotas = t… (10 letters) quiet = e… (9 letters) foils = f… (7 letters) score = s… (11 letters)

Answers
taper = perpetrate (10 letters) heals = seashells (9 letters) brows = borrows (7 letters) often = footnote (8 letters) farce = carefree (8 letters) yowls = slowly (6 letters) satin = assistants (10 letters) awful = lawful (6 letters) iotas = tattooists (10 letters) quiet = etiquette (9 letters) foils = fossils (7 letters) score = sorceresses (11 letters)

Workings

Hint
One of the words is waterfall (wat + erf + all).

Answers
som + eth + ing = something
hai + rbr + ush = hairbrush
gra + ssl + and = grassland
pin + eap + ple = pineapple
pol + ice + man = policeman
mea + nwh + ile = meanwhile
wat + erf + all = waterfall
sca + rec + row = scarecrow
yes + ter + day = yesterday
obs + tin + ate = obstinate