G8

Grade 8 Unit 1 Lesson 7 P TE

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Homework

Unit 1 · Lesson 7: Estimate Irrational Numbers

Objective: I will estimate the decimal of an irrational square root.

Vocabulary Steps:

Square Numbers (Perfect Square): the result after

multiplying an integer by itself

Irrational Numbers: the set of all numbers that

cannot be written as a ratio of two integers; it cannot

be written as a simple fraction because the decimal is

non-terminating and non-repeating

0.101101110... , �^23 ,π,√ 10 ,√1.6,−√ 123

Square Root: the square root of a number is a value

that, when multiplied by itself, gives the number

1. Find the perfect square immediately above
   and below your number.


2. The answer will be between the square roots
   of these two numbers.


3. Estimate the decimal based on how close
   your number is to each of the squares.

Example # 1

Directions: Estimate the decimal value. Use a calculator to check.

√ 40

Solution:

• When considering √ 40 on a number line, the perfect square less than 40 is 36.


• √ 36 = 6


• The perfect square greater than 40 is 49.


• √ 49 = 7


• Now I can make the statement√ 36 < √ 40 < √ 49.


• Simplify 6 <√ 40 < 7

• (^) √ 40 is between 6 and 7 or 6 <√ 40 < 7

• Calculator: √ 40 ≈6.3

Example # 2

−√ 28

2

Solution:

• −√ 228 =(−1) 2 ⋅√^28


• √^252 <√^282 <√^362


• 52 <√ 228 <^62


• 2.5 <√^282 < 3


• √^282 will fall between 2 and 3.


• Since it is negative, it will fall between -2 and -3 or −3 <−√ 228 <− 2 .= ─2.6

Name: ___

Date: ___