Random Puzzles 

Workings

Hints
The first letters of the words are: A, C, D, D, I, L, M, N, P, R.

Answers
acq + uit + tal = acquittal
con + duc + tor = conductor
dec + kch + air = deckchair
dif + fer + ent = different
imp + ort + ant = important
lig + htn + ing = lightning
myt + hol + ogy = mythology
new + sag + ent = newsagent
pol + ice + man = policeman
rec + tan + gle = rectangle

Workings

Hint
The cube root of the given number is a good starting point.

Answer
71, 73, 79.

Reasoning
The cube root of 409,457 is around 74.

The closest consecutive prime numbers to 74 are: 61, 67, 71, 73, 79, 83, 89, 97.

Using a calculator, it is quickly seen that the answer can only be found using 71, 73 and 79.

Workings

Hint
The 2^nd word begins with the letter B.

Answers
a-a-e = amaze (MZ) --ave = brave (BR) -uie- = quiet (QT) --gon = wagon (WA) p--ot = pivot (IV) vi-e- = vixen (XN) -ac-t = yacht (YH) --met = comet (CO) b--ep = bleep (LE) -u-ge = judge (JD) -lan- = flank (FK) -ra-e = grape (GP) bon-- = bonus (US)
This puzzle isn't guaranteed to have a unique answer, can you find another?

Workings

Hint
The first word begins with L.

Answer
Look before you leap.

Using the initial letters of each word.