To simplify these expressions, we can simplify each square root individually and then combine them.

For the first expression, we simplify each square root:

√1/12 = √(1/4 * 1/3) = √1/4 * √1/3 = 1/2 * √1/3 = √1/3 / 2

√3/4 = √(3/4) = √3 / √4 = √3 / 2

√75/49 = √(25/49 * 3) = √25/49 * √3 = 5/7 * √3

Now we can combine the simplified square roots:

√1/12 + √3/4 + √75/49 = √1/3 / 2 + √3 / 2 + 5/7 * √3

To add these terms, we need to have a common denominator for the fractions:

√1/3 / 2 + √3 / 2 + 5/7 * √3 = (√1/3 + √3) / 2 + 5/7 * √3

To add the fractions, we need to have a common denominator of 14:

(7 * √1/3 + 7 * √3) / 14 + 10/14 * √3

Simplifying the numerator:

(7√1 + 7√3) / 14 + 10/14 * √3

Combining the terms:

(7√1 + 7√3 + 10√3) / 14

Simplifying the numerator:

(7 + 17√3) / 14

Therefore, the simplified expression is (7 + 17√3) / 14.

For the second expression, we simplify each square root:

√20/9 = √(4/9 * 5) = √4/9 * √5 = 2/3 * √5

√180 = √(36 * 5) = √36 * √5 = 6 * √5

√80/9 = √(16/9 * 5) = √16/9 * √5 = 4/3 * √5

Now we can combine the simplified square roots:

√20/9 + √180 - √80/9 = 2/3 * √5 + 6 * √5 - 4/3 * √5

To add these terms, we need to have a common denominator for the fractions:

2/3 * √5 + 6 * √5 - 4/3 * √5 = (2√5 + 18√5 - 4√5) / 3

Simplifying the numerator:

(2 + 18 - 4)√5 / 3

Combining the terms:

16√5 / 3

Therefore, the simplified expression is 16√5 / 3.