Answer:
< then >
Explanation:
11 7/8 can be written as (11 + 7/8). If we find (11+7/8)², we know that √(11+7/8)² = (11+7/8), so we can compare (11+7/8)² with 129 and see which is bigger.
(11+7/8)² = (11+7/8) * (11+7/8)
= 121 + 7/8 * 11 + 7/8 * 11 + (7/8)²
= 121 + 77/8 + 77/8 + (7/8)²
77/8 is greater than 9 (8*9 = 72) but less than 10 (8*10=80). Rounding down to 7, we have
121 + 7 + 7 + (7/8)²
= 135 + (7/8)²
Even when rounding down, (11+7/8)² is greater than 129. Therefore,
129 < (11+7/8)²
square root both sides
√129 < (11+7/8)
We can apply a similar process for the next one.
(3+5/6)² = (3+5/6) * (3+5/6)
= 9 + 5/6 * 3 + 5/6 * 3 + (5/6)²
= 9 + 15/6 + 15/6 + (5/6)²
15/6 is less than 3 (6*3 = 18) but greater than 2 (6*2 = 12). Rounding down to 2, we have
9 + 2 + 2 + (5/6)²
= 13 + (5/6)² > 10
Even when rounding down, (3+5/6)² is greater than 10
(3+5/6)² > 10
square root both sides
(3+5/6) > √10