The tutor returns to a “favourite” topic of high school math.

High school math students may soon be posed a question similar to the following:

Estimate to one decimal place, without a calculator, the square root of 55.

Note that square root can also be expressed as “to the half power”.

Solution:

49^0.5=7 and 64^0.5=8, so we know that 55^0.5 lies between 7 and 8. However, what is the decimal? We find it as follows:

64-49=15, while 55-49=6. Therefore, 55 is 6/15=0.4 of the way from 49 to 64. We then accept the decimal part to be 0.4, so our estimate of 55^0.5 is 7.4, to one decimal place.

Checking on the calculator, 55^0.5=7.416198487: rounded properly to one decimal place, this agrees with our estimate:)

I’ll be commenting more on math estimation techniques as we get back into regular season.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.