In this activity, we will use trial and improvement to solve equations.

Example

Solve a² = 54 giving the answer to 1 decimal place.

Answer

Try a value you think will be close to the answer.

a = 7   a² = 49   This is too small. Try a bigger value.
a = 8   a² = 64   This is too big. Try between 7 and 8.
a = 7.5  a² = 56.25   Now let's try halfway. Too big. Try a smaller number.
a = 7.3   a² = 53.29   Too small.
a = 7.4   a² = 54.76   Too big.
a = 7.35   a² = 54.02   Let's try halfway between 7.3 and 7.4. Too big. 

The value of a is closer to 7.3 than 7.4 

Answer to 1 decimal place is a = 7.3

Let's have a go at some questions now.