Download 8-2

8-2 Estimating Roots
Objective: Students will be able to use roots to
estimate solutions.
8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational
numbers, locate them approximately on a number line diagram, and estimate the value of
expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2
is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better
approximations.
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the
form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small
perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Do Now:
Write The Following In Exponential Form Then Solve:
1) 4*4
2) 3*3*3
3) 5*5*5
4) 6*6
5) 7*7
6) -10*-10*-10
7) -2.5*-2.5
2
x
Squaring: to raise a number
to the second power
Cubing: to raise a number
to the third power.
x
x
2
Square Root: one of the two
equal factors of a number

3
3
x
3
Cube Root: one of the three
equal factors of a number
Perfect Square: a rational number
whose square root is
a whole number
x a
2
 ax
(5)  25
2
25  5
Non-Perfect Square: a number
whose square root is not
a whole number
 (decimal/fraction) 
13  3.6055...
Perfect Cube: a rational number
whose cube root is
a whole number
x a
3
3
2 8
ax
3
3
8 2
Non-Perfect Cube: a number
whose cube root is not
a whole number

(decimal,
fraction)
3
14  2.4101...
Find Each Square or Cube Root
Perfect Square Roots
Perfect Cube Roots
Estimating Square and Cube Roots:
You can estimate the value of a square or cube root by
determining which two perfect squares or cubes the number
falls in between.
Estimate
3 100
83

Worksheets!
Homework 8-2
Pages 85-86 All #’s
Exit Ticket:
After an accident, officials used the formula below to
estimate the speed the car was traveling based on the
length of the car’s skid marks. Where s represents the
speed in miles per hour and m is the length of the
skid marks in feet.
s  24m
If a car leaves a skid mark of 50 feet, what was its
approximate speed?
