You can add or subtract (and divide if positive) same value to both sides of an inequality, it doesn't change the balance but makes it easier to decide.
#1 <
√3 + 2 vs √3 + 3
2 < 3
#2 >
√11 + 15 vs √8 + 15
√11 > √8
#3 <
√6 + 5 vs 6 + √5
√6 - √5 vs 6 - 5 = (√6 + √5)(√6-√5)
1 < √6 + √5
#4 <
√9 + 3 vs 9 + √3
3 + 3 = 6 < 9 + √3
This can be solved similarly to #3 too
#5 >
√17 - 3 vs -2 + √5
√17 - 3 > 4 - 3 = 1 and √5 - 2 < 3 -2 = 1
Left side is greater than 1, right side is smaller than 1
