Estimating with roots

• What is the result of \(5 \times 9\)?


  45
• What is \(12.5 \times 8.4\) equal to?


  105
• What is the result of \(125 \times 84\)?


  10500
• What is the value of \(17\) in the context of roots?


  1
• How do you expand \(3x(4x - 3)\)?


  By distributing \(3x\) to both terms inside the parentheses
• What is \(120\%\) of £44?


  £19.80
• How do you calculate \(45\%\) of £44?


  By multiplying £44 by \(0.45\)
• What is the formula for calculating \(5\%\) of a number?


  Multiply the number by \(0.05\)
• How do you solve the equation \(4x - 6 = 42 - 2x\)?


  By isolating \(x\) on one side of the equation
• What is the solution for \(x\) in the equation \(2x = 40\)?


  x = 20
• How do you make \(x\) the subject of the equation \(y = \frac{x}{yx}\)?


  By multiplying both sides by \(yx\)
• What is the nth term of the sequence \(0.4, 0.8, 1.2, 1.6\)?


  0.4n
• How do you calculate \((5 + 5)^2 \div (2 \times 3)\)?


  By first calculating \(10^2\) and then dividing by \(6\)
• What is the area of a square with side length \(7\text{ cm}\)?


  49 cm²
• What does it mean when \(x\) is between \(2\) and \(3\)?


  It indicates that \(x\) is greater than \(2\) but less than \(3\)
• What is the value of \(1^2\)?


  1
• What is the value of \(2^2\)?


  4
• What is the value of \(3^2\)?


  9
• What is the value of \(4^2\)?


  16
• What is the value of \(5^2\)?


  25
• What is the value of \(6^2\)?


  36
• What is the value of \(7^2\)?


  49
• What is the value of \(8^2\)?


  64
• What is the value of \(9^2\)?


  81
• What is the value of \(10^2\)?


  100
• What is the value of \(11^2\)?


  121
• What is the value of \(12^2\)?


  144
• What is the value of \(1^3\)?


  1
• What is the value of \(2^3\)?


  8
• What is the value of \(3^3\)?


  27
• What is the value of \(4^3\)?


  64
• What is the value of \(5^3\)?


  125
• What is the value of \(6^3\)?


  216
• What is the value of \(7^3\)?


  343
• What is the value of \(8^3\)?


  512
• To find the square root, we need to solve x^2 = b
• Estimating square roots is a useful skill in quickly approximating calculations without a calculator.
• The root is the value that makes an equation equal to zero.
• One method to estimate square roots is by averaging the two nearest perfect squares.
• Estimating square roots involves finding the two perfect squares the number falls between.