Use the number line to estimate a value for 35 3 .

Given number: 35 3 Now, 3 3 = 27 and 4 3 = 64 ∴ 27 < 35 < 64 ∴ 27 3 < 35 3 < 64 3 ∴ 3 < 35 3 < 4 Find halfway between 27 and 64 . 27 + 64 2 = 91 2 = 45 . 5 35 is closer to 27 than 64 . 35 3 is closer to 3 than 4 . ∴ A sensible estimate 35 3 would be 3 . 2 or 3 . 3 .

Use the number line to estimate a value for 35 3 .

Given number: 35 3 Now, 3 3 = 27 and 4 3 = 64 ∴ 27 < 35 < 64 ∴ 27 3 < 35 3 < 64 3 ∴ 3 < 35 3 < 4 Find halfway between 27 and 64 . 27 + 64 2 = 91 2 = 45 . 5 35 is closer to 27 than 64 . 35 3 is closer to 3 than 4 . ∴ A sensible estimate 35 3 would be 3 . 2 or 3 . 3 .

Use the number line to estimate value for 54 3 .

Given number: 54 3 Now 3 3 = 27 and 4 3 = 64 ∴ 27 < 54 < 64 ∴ 27 3 < 54 3 < 64 3 ∴ 3 < 54 3 < 4 Find halfway between 27 and 64 . 27 + 64 2 = 91 2 = 45 . 5 54 is closer to 64 than 27 . 54 3 is closer to 4 than 3 ∴ A sensible estimate of 54 3 would be 3 . 7 or 3 . 8 .

Use the number line to estimate a value for 100 3 .

Given number: 100 3 Now 4 3 = 64 and 5 3 = 125 ∴ 64 < 100 < 125 ∴ 64 3 < 100 3 < 125 3 ⇒ 4 < 100 3 < 5 Find halfway between 64 and 125 . 64 + 125 2 = 189 2 = 94 . 5 100 is closer to 125 than 64 . ∴ 100 3 is closer to 5 than 4 . ∴ A sensible estimate 100 3 would be 4 . 6 or 4 . 7 .