Square Numbers and Area Models
Find the area of a square with each side length.
a) 7 units
7 x 7 =49 units squared
What is 112 ?
121
Using a number line decide the placement for a good estimate of the square root of 27.
5.2
Which types of triangles does the Pythagorean Theorem apply to.
Right angle triangles.
Give an example of the pythagorean triples.
Show that 16 is a square number.
Use a diagram, prime factorization, or common factor
2 x 2 x 2 x 2
1, 2, 4, 8, 16 odd number of factors
By listing the factors in ascending order of 40 determine if it is a perfect square or not.
1, 2, 4, 5, 8, 10, 20, 40
even number of factors and therefore it is NOT a perfect square.
Which two consecutive numbers is each square root between?
square root of 72.
8 and 9
Find the length of the unmarked side in each right triangle.
Give your answers to one decimal place.
side a = 3 cm
side b = 6 cm
side c = ?
6.7cm
Each set of measurements below represents the side lengths of a triangle.
Identify which triangles are right triangles.
How do you know?
a) 3 cm, 4 cm, 6 cm
not a right angle as the sum of the squares of the sides are smaller than the square on the hypotenuse.
These numbers are not square numbers.
Which two consecutive square numbers is each number between?
a) 50
49 and 64
The factors of each number are listed in ascending order.
Which numbers are square numbers?
Find a square root of each square number.
a) 216: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
b) 196: 1, 2, 4, 7, 14, 28, 49, 98, 196
c) 441: 1, 3, 9, 21, 49, 147, 441
b 14
c 21
Is each statement true or false? Explain.
square root of 19 is between 18 and 20.
square root of 101 is greater than 10.
false 4.35
true 10.01
Find the length of the unmarked side in each right triangle.
Give your answers to one decimal place.
side a = ?
side b = 4 cm
side c = 8 cm
6.9 cm
Find the length of the unmarked side in each right triangle.
Give your answers to one decimal place.
side c = 17
side b = 16
side a = ?
5.7
I am a two-digit square number. The sum of my digits is 13.
What square number am I?
49
Find a number whose square root is 24.
576
Chess is played on a square board.
A particular board has an area of about 3250 cm squared
What are the approximate dimensions of the board to two decimal places?
57.01 cm x 57.01 cm
Find the length of the diagonal, d, in each rectangle.
Give your answers to two decimal places where needed.
side lengths are 12m and 5m
13 m
Jovi is laying a foundation for a garage with dimensions 10 m by 6 m.
To check that the foundation is square, Jovi measures a diagonal.
How long should the diagonal be?
Give your answer to one decimal place.
11.67 m
A square patio has area 225 m2
a) Find the dimensions of the patio.
b) The owner wants to put lights around the patio.
How many metres of lighting is needed?
c) Each string of lights is 25 m long.
How many strings of lights are needed?
15 m by 15 m
15 x 4 =60 60 meters of lights
60/25 =2.4 string of lights
Find the square root of each number.
a) 1222
b) 1522
c) 3722
122
152
372
A farmer has 600 m of fencing.
He wants to enclose a square field of area 24 200 m squared
What are the approximate dimensions of the field?
Give your answer to one decimal place.
Does the farmer have enough fencing to enclose the field?
155.6 m
yes he has enough fencing to enclose the field.
Find the length of the diagonal, d, in each rectangle.
Give your answers to two decimal places where needed.
side lengths are 13m and 8m
15.3m
A cat is stranded in a tree.
You lean a 10-m ladder against the tree.
It is 2 m from the base of the tree.
How far up the tree does the ladder reach?
Give your answer to one decimal place.
9.8 m