Approximating square roots

The  exercise appears under the Pre-algebra Math Mission. This exercise cultivates an ability to mentally estimate square roots.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the integers that the square root is between: This problem provides the square root of a number that is not a perfect square. The student is asked to determine between which two consecutive integers the square root of the number is located.Esr1.png

Strategies
Knowing the times tables, in particular the square numbers, would assist in completing this exercise accurately and efficiently.
 * 1) The squares through $$12^2=144$$ have been seen to show up from research.

Real-life Applications

 * 1) An ability to estimate things mentally is an important skill for quantitative reasoning in general. For example, it can be used to determine if an error has come up in calculation.
 * 2) Square roots come up in applications of the Pythagorean Theorem which leads to trigonometry.