Square Numbers
Find the area of a square with the side length of 64mm
642 or 64 x 64 = 4096
What is a square root? Give an example.
A square root is a number is the product of a mathematical expression with two identical factors.
ex) 8 x 8 = 64
The set of measurements below represent the side lengths of a triangle. ID which triangles are right triangles. How do you know?
a) 3cm, 4cm, 6cm
b) 6cm, 8cm, 10cm
25cm does not = 36cm, therefore NOT a right triangle.
b)a2 + b2 = c2
6cm2 + 8cm2 = 10cm2
36cm + 64cm = 100cm
100cm = 100cm SO (b) is a right triangle!
An oak tree is 15 metres tall and a bird is standing on the ground 8 metres from the tree. If the bird flies directly to the top of the tree, how far will it fly?
a2+b2=c2
152+82=c2
225m+64m=c2
289m=c2
17m = c
The bird will fly 17 meters if it flies directly to the top of the tree.
Which of these numbers is a perfect square? How do you know?
a) 14
b) 60
c) 36
a) NOT
b) NOT
c) = perfect square b/c 6x6=36
Find a number whose square root is 24
If the square root = 24
24 x 24 = 576
Which sets of numbers below are Pythagorean triples?
a) 20, 21, 29 b) 11, 34, 35
a) 202+212=292
400+441=841
841=841
b) 112+342=352
121+1156=1225
1277 DOES NOT = 1225
Two cars meet at an intersection. One travels north at an average speed of 80km/hr. The other travels east at an average speed of 55km/hr. How far apart are the cars after 3 hours? Give your answer to one decimal place. No Calculator for this one!
Draw Diagram. See the board:
a2+b2=c2
55km2+80km2=c2
3025km+6400km=c2
/[9425km=c2
97.1km/h x 3hrs = 291.2km
The cars are 97.1kms apart after 3 hours.
I am a two-digit square number. The sum of my digits is 13.
What square number am I?
49
Find the square of /[841
Squaring a square root cancels out the square root function so your answer is: 841
Two numbers in a Pythagorean triple are 77 and 85. Find the third number.
36
Ms. Francisco uses a ruler and compass to construct a triangle with side lengths 3cm, 5cm, and 7cm. Before Ms. Francisco constructs the triangle, how can she tell if the triangle will be a right triangle? Explain.
32+52=/ 72
IOW 34 does not equal 49
The measurements do not satisfy the Pythagorean Theorem, so it is NOT a right triangle.
These numbers are not square numbers.
Which two consecutive square numbers is each number between?
a) 7 b) 30 c) 50
a) 4 and 9
b) 25 and 36
c) 49 and 64
Are these statements true or false? Explain.
a) \[19 is between 18 and 20.
b) \[101 is greater than 10.
a) The square root of 19 = 4.4 so statement a is FALSE. Or, square root of 19 falls between the whole numbers 4 and 5.
b) The square root of 101= 10.05 so statement b is TRUE.
See the board
The perimeter of a right triangle is 90m. The length of the longest side of the triangle is 41m. Find the lengths of the other two sides. How did you find out?
We know: Hypotenuse=41m Perimeter=90m
90-41=49 so the two missing legs must add up to 49
Since 9+40+41=90
92+402=412
81+1600=1681
1681=1681 CORRECT
The other two sides of the triangle must be 9m and 41m because the values satisfy Pythagorean Theorem.
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?
a) Dimensions = /[225m = 15m
b) 15x4=60m of lights
c) 60 % 25=2.4 strings of lights are needed if 1 string is 25 meters.
Micaiah wants to build his own chess board. A typical chess board has an area of 3250cm2. What approximate dimensions should Micaiah's chess board be to 2 decimal places?
A[] = l2
l=/[A
Find the square root of 3250cm
Answer = 57.01
What are the steps to solve a question that has a diagram of a right triangle with squares drawn on each leg and the hypotenuse. The area of the two "leg squares" are 22m2 and 10m2. The question asks: Find the area of each indicated square. See the board for the diagram.
Steps 2 Solve:
1) Formulas needed are: A[]=square root of l and a2+b2=c2
2) Calculate the side length of the two leg squares
3) Plug in variables into pythagorean formula
4) Solve for missing variable
5) Square the missing variable to find the area of the missing square.
6) Indicate final answer.
I am a square number. The sum of my digits is 9. What square numbers might I be? List ALL possible answers!
Answers can be:
9, 36, 81, 144, 225, or 324