Use the number line to estimate a value for 40 .

Given number: 40 We know, 6 2 = 36 and 7 2 = 49 Now, 36 < 40 < 49 ∴ 36 < 40 < 49 and 36 = 6 , 49 = 7 Therefore, 6 < 40 < 7 Now, 40 is the number between 36 and 49 . ∴ 40 is the number between 6 and 7 . Finding halfway between 36 and 49 : 36 + 49 2 = 85 2 = 42 . 5 40 is closer to 36 than 49 . ⇒ 40 is closer to 6 than 7 . ∴ A sensible estimate of 40 will be 6 . 3 and 6 . 4 .

Use the number line to estimate a value for 70 .

Given number: 70 We know, 8 2 = 64 and 9 2 = 81 Now, 64 < 70 < 81 ∴ 64 < 70 < 81 and 64 = 8 , 81 = 9 Therefore, 8 < 70 < 9 Now, 70 is the number between 64 and 81 . ∴ 70 is the number between 8 and 9 . Finding halfway between 64 and 81 : 64 + 81 2 = 145 2 = 72 . 5 70 is closer to 64 than 81 . 70 is closer to 8 than 9 . ∴ A sensible estimate of 70 will be 8 . 3 and 8 . 4 .

Use the number line to estimate a value for 93 .

Given number: 93 We know, 9 2 = 81 and 10 2 = 100 Now, 81 < 93 < 100 ∴ 81 < 93 < 100 and 81 = 9 , 100 = 10 Therefore, 9 < 93 < 10 Now, 93 is the number between 81 and 100 . ∴ 93 is the number between 9 and 10 . Finding halfway between 81 and 100 : 81 + 100 2 = 181 2 = 90 . 5 93 is closer to 100 than 81 . 93 is closer to 10 than 9 . ∴ A sensible estimate of 93 will be 9 . 6 and 9 . 7 .

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 .

E M B I B E

Cambridge Lower Secondary Maths Stage 9: Student's Book>Number and Calculation>Chapter 11 - Square Roots, Cube Roots and Calculation>Exercise 1

Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 1

Author:Michele Conway, Belle Cottingham, Alastair Duncombe & Amanda George

Michele Conway Mathematics Solutions for Exercise - Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 1

Attempt the practice questions from Exercise 4: Exercise 1 with hints and solutions to strengthen your understanding. Cambridge Lower Secondary Maths Stage 9: Student's Book solutions are prepared by Experienced Embibe Experts.