G8

Copyright © Swun Math Grade 8 Unit 1 Lesson 6 C TE

Input/Model

(Teacher Presents)

Directions: Determine if the expression is a perfect square. If not, determine the two perfect

squares that the square root lies between.

1. (^) √ 4
   Solution:

• A square is a plane figure with four equal sides and angles. To prove that 4 is a perfect square, build a square that has
  an area of 4.


• When creating a perfect square with an area of 4, the length needs to be 2 and the width needs to be 2.


• The integer multiplied by itself to have a product of four is 2.

• (^) √ 4 is the same as (^) √ 2 ⋅ 2. This indicates that the square root of 4 is 2.

• 22 = 2⋅2 = 4, therefore


• √ 4 =√ 2 ⋅ 2 = 2

Answer: Since 2 is a whole number, (^) √ 4 is a rational number.

2. √ 20

Solution:

• 20 is not a perfect square and this can be proved since a square cannot be built with an area of 20


• Since √ 20 is not a perfect square, to best estimate its value, we need to identify what two perfect squares it lies in
  between.


• 20 lies between 16 and 25, which are both perfect squares.

• Since (^) √ 16 = 4 and √ 25 = 5, (^) √ 20 must lie between 4 and 5.
Answer: Since √ 20 is an irrational number, √ 20 lies between 4 and 5.
4
5

• 1 0 1 2 3 4 5 6 7 8 9 10 11 12
  roots

squares

16 20 25