# 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