Reasoning About Square Roots: IM 8.8.5
[url=https://im.kendallhunt.com/MS/teachers/3/8/5/preparation.html]“Reasoning About Square Roots”[/url] from IM Grade 8 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 8.8.5
- IM 8.8.5 Lesson: Reasoning About Square Roots
- Practice 8.8.5
- IM 8.8.5 Practice: Reasoning About Square Roots
IM 8.8.5 Lesson: Reasoning About Square Roots
Check all of the TRUE statements.
What two whole numbers does each square root lie between? Explain your reasoning.
[size=150][math]\sqrt{7}[/math][/size]
[math]\sqrt{23}[/math]
[math]\sqrt{50}[/math]
[math]\sqrt{98}[/math]
Can we do any better than “between 3 and 4” for [math]\sqrt{12}[/math]? Explain a way to figure out if the value is closer to 3.1 or closer to 3.9.
The numbers x, y, and z are positive, and x²=3, y²=16, and z²=30. Plot x, y, z and -√2 on the number line. Be prepared to share your reasoning with the class.
IM 8.8.5 Practice: Reasoning About Square Roots
Explain how you know that [math]\sqrt{37}[/math] is a little more than 6.
Explain how you know that [math]\sqrt{95}[/math] is a little less than 10.
Explain how you know that [math]\sqrt{30}[/math] is between 5 and 6.
Plot each number on the number line: 6, √83, √40, √64, 7.5
[size=150]The equation[math]x^2=25[/math] has [i]two[/i] solutions. This is because both[math]5\cdot5=25[/math], and also [math]\text{-}5\cdot\text{-}5=25[/math]. . So, 5 is a solution, and also -5 is a solution.[/size][br][br]Select [b]all[/b] the equations that have a solution of [math]\text{-}4[/math]:
Find all the solutions to each equation.
[math]x^2=81[/math]
[math]x^2=100[/math]
[math]\sqrt{x}=12[/math]
Select all the irrational numbers in the list.
Each grid square represents 1 square unit. What is the exact side length of the shaded square?
For each pair of numbers, which of the two numbers is larger?
Estimate how many times larger.
For each pair of numbers, which of the two numbers is larger?
Estimate how many times larger.
For each pair of numbers, which of the two numbers is larger?
Estimate how many times larger.
The scatter plot shows the heights (in inches) and three-point percentages for different basketball players last season. Circle any data points that appear to be outliers.
Compare any outliers to the values predicted by the model.