Irrational numbers, such as roots, can also be represented on a straight line.

For example, follow these steps to work out the point which represents the number Ö2  

• Draw a square on the straight line whose side is the unit segment between 0 and 1. According to Pythagoras' theorem the diagonal of the square is equal to Ö2.

• Use a compass to translate this diagonal line onto the straight line. The point where the arc cuts the straight line represents the number Ö2.

6. You can use this method of constructing squares or rectangles to find the square roots of many whole numbers. Draw a rectangle with sides measuring 2 and 3 into your exercise book. Its diagonal is equal to the square root of 13.

Use the arrows to change the base and height values.

Look at the drawing in the window to see what the drawing in your exercise book should look like.

Represent the following numbers in the same way: Ö5,  Ö10, Ö20 and Ö34.

Use the window to check that your drawings are correct.