# Estimation

## Evaluating Square Roots by Hand

Square roots commonly are irrational numbers, so that it is necessary to estimate them. Usually today, we use a calculator to find them. Many students, however, are curious about how they could do it without a calculator. Here I want to reverse the usual format of this blog, presenting a summary I have written that …

## The Method of False Position: Old and New

(An archive question of the week) Last time, as part of our series on estimation, we looked at some numerical methods for solving equations approximately. I mentioned the Method of False Position, but when I looked for more detailed expositions in our archive, I realized that in a sense it is really two different things, …

## Numerical Approximation Methods: When Algebra Doesn’t Work

The problems students see in class are usually only those that can be solved by the methods they have been taught. Too many students conclude that algebra can solve anything! But the reality is that if you just wrote an equation at random, it probably could not be solved algebraically. When students ask us about …

## Estimation vs. Other Ways to Check Subtraction

(An archive question of the week) Last time I looked at reasons for learning to estimate. In searching for answers on that topic, I ran across a question that touches not just on reasons for estimation, but on other ways to check an answer, and on some of the specific ideas we will be looking …

## Estimation: The Value of Imprecision

Many questions we have received have been about various aspects of estimation. Often this topic has been downplayed, because we tend to think of math as being all about precision; but it is essential in many applications, sometimes because there is nothing else to do, and other times because exactness wastes effort. I am starting …