Graphs, Square Numbers and Square Roots

This activity shows how square numbers plotted on a graph can help with calculations – or close estimates – of square roots and the squares of decimal numbers.
 With a sheet of graph paper in portrait position, children draw x and y axes (arrowed at the ends to indicate that the scales could continue).
 The x axis is numbered on the cm lines from the origin 0 to 15 or as far as it will go and labelled ‘Number (square root)’.
 The y axis is numbered on the cm lines from the origin 0 in tens to 200 or as far as it will go and labelled ‘Square number’.
 Explain that the graph will begin at the origin as 02 is 0.
 Ask the children to plot the squares of all whole numbers and join them to make as smooth a curve as possible.
 Show how, say, 6.82, can be calculated by following 6.8 on the x axis up to the drawn line and reading off the answer on the y axis. An accurately drawn and read graph would produce an answer between 45 and 47.
 In reverse, square roots can be shown.Taking √90 as an example, follow the 90 line on the y axis to the drawn line and read down to the x axis. In this case, a reasonably accurate answer would be about 9.5.
 Ask children to use the graph to calculate more squares and square roots, checking accuracy on calculators