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*42) 3*3*33) 5*5*54) 6*6 5) 7*7 6) -10*-10*-107) -2.5*-2.5

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x 2

€

x 3

Squaring: to raise a numberto the second power

Cubing: to raise a numberto the third power.

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x 2

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x 33

Square Root: one of the twoequal factors of a number

Cube Root: one of the three equal factors of a number

Perfect Square: a rational number whose square root is

a whole number

Perfect Cube: a rational number whose cube root is

a whole number

Non-Perfect Square: a number whose square root is not

a whole number(decimal/fraction)

Non-Perfect Cube: a numberwhose cube root is not

a whole number(decimal, fraction) €

x 3 = a

a3 = x

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23 = 8

83 = 2

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x 2 = a

± a = x

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(±5)2 = 25

25 = ±5

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13 = ±3.6055...

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143 = ±2.4101...

Find Each Square or Cube Root

Perfect Square Roots Perfect 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.

Estimating Square and Cube Roots:

Estimate

€

83

€

1003

Worksheets!

Homework 8-2Pages 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.

If a car leaves a skid mark of 50 feet, what was its approximate speed?

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s = 24m