1. For the first....just add the 4 and 6 and append the radical...so we have...
10 4√ [ 2x ] ⇒ first answer
2. A little trickier, NSS
Ratio 3 : 2 means that there are 3 + 2 = 5 equal parts......and the longer piece is 3 of these parts
So......the longer piece =
(3 /5) √250 =
(3/5) √ [ 125 * 2 ] =
(3/5) √ ( 25 * 5 * 2 ] =
(3/5) √ 25 * √5 * √2 =
(3/5) * 5 * √10 =
3 √ 10 units