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 root of a number is the inverse of taking the power. The guess of the 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.


1. Estimate 4.4223.

Answer: 64

4 x 4 x 4 = 64. The actual answer to 4.4223 is 84.468 (to 3dp).

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

Answer: 25

Guess 20 as a starting value.

Estimating 4th root of 160 000

Note: the answer is either 24 or 25 (to 2 significant figures). Test 24.5 as the boundary between 24 and 25: that is also too low therefore the number must be higher than 24.5, round up for an answer of 25.