Estimating Powers and Roots

## Estimating Powers and Roots

Estimating the power of a number involves rounding the number to one significant figure (1sf) and multiplying that number a suitable number of times.

Estimating the root of a number uses a technique known as Trial and Improvement. The calculation works by taking a guess at the answer. The guess of that answer is raised to that power and checked against the original number. The guess is revised, and the calculation repeated until sufficient accuracy is obtained.

Trial and Improvement is best calculated using a table.

## Example 1

Estimate 4.4223.

Round 4.422 to 1 significant figure 4 x 4 x 4 = 64. The actual answer to 4.4223 is 84.468 (to 3dp).

Estimate the value of root(4)366218 to 2 significant figures.