Lesson 5Reasoning About Square Roots
Learning Goal
Let’s approximate square roots.
Learning Targets
When I have a square root, I can reason about which two whole numbers it is between.
Lesson Terms
- square root
Warm Up: True or False: Squared
Problem 1
Decide if each statement is true or false.
Activity 1: Square Root Values
Problem 1
What two whole numbers does each square root lie between? Be prepared to explain your reasoning.
Are you ready for more?
Problem 1
Can we do any better than “between 3 and 4” for
Activity 2: Solutions on a Number Line
Problem 1
The numbers
Plot
, , and on the number line. Be prepared to share your reasoning with the class. Plot
on the number line.
Lesson Summary
In general, we can approximate the values of square roots by observing the whole numbers around it, and remembering the relationship between square roots and squares. Here are some examples:
is a little more than 8, because is a little more than and . is a little less than 9, because is a little less than and . is between 8 and 9 (it’s 8 point something), because 75 is between 64 and 81. is approximately 8.67, because .
If we want to find a square root between two whole numbers, we can work in the other direction. For example, since
Many calculators have a square root command, which makes it simple to find an approximate value of a square root.