Question

Select the correct inequality sign to make the statements true.

Answer 1

Answer:

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Step-by-step 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