Powers and rootsEstimating powers and roots

Powers

Powers of any number can be estimated by finding the nearest integers above and below the number.

Example

Estimate the value of 3.7³

3.7 is between 3 and 4.

3³ = 27 and 4³ = 64, so the value of 3.7³ will be between 27 and 64, and closer to 64 than 27 because 3.7 is closer to 4 than 3.

So an estimate for 3.73 would be 50 (the actual value is 50.653).

Roots

Roots can be estimated by finding the roots of numbers that have integer values above and below the number.

Example

Estimate the value of √53

This means that the value of √53 is between 7 and 8, and closer to 7 because 53 is closer to 49 than it is to 64.

So an estimate for √53 is 7.3 (the exact value is 7.280…).