When using trial and improvement guess what the answer might be, then improve on it until you get close to the correct answer.
A square has an area of 20 cm^{2}. Use a method of trial and improvement to find the length of its side, correct to 1 decimal place (1 d.p.).
Start by trying 4:
4 × 4 = 16 (too small)
4 is too small, so try 5:
5 × 5 = 25 (too big)
4 is too small, and 5 is too big, so the answer lies between 4 and 5.
Try 4.5:
4.5 × 4.5 = 20.25 (too big)
Try 4.4:
4.4 × 4.4 = 19.36 (too small)
Therefore, the answer lies between 4.4 and 4.5, but it is closer to 4.5.
So the answer is 4.5cm to 1 d.p.
The question asked us to find the length of the side correct to 1 d.p., so you only need to try values with 1 d.p.
If, however, the question had asked for values correct to 2 d.p. you would have got a more accurate answer. For example:
4.45 × 4.45 = 19.80 (too small)
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