Name: ____________________ Math 8 Date: _____________

Unit 1 - Perfect squares and cubes Lesson 1.2 - Estimating Square Roots

Learning Intention: Develop strategies for estimating a square root.

1- A square root of a given number is a number when multiplied by itself results in the given number. in simple terms it just means this:

SQUARE OF A NUMBER: The Square of a number is that number raised to the power 2.

Examples: Square of 9 = 92 = 9 x 9 = 81

Square of 0.2 = (0.2)2 = (0.2) x (0.2) = 0.04

PERFECT SQUARE: A natural number is called a perfect square, if it is the square of some

natural number.

Some Properties of Squares of Numbers 1. The square of an even number is always an even number.

Example: 2 is even and 22 = 4, which is even.

2. The square of an odd number is always an odd number.

Example: 3 is odd and 32 = 9, which is odd.

3. The square of a proper fraction is a proper fraction less than the given fraction.

Example: 𝑆𝑞𝑢𝑎𝑟𝑒 𝑜𝑓 (1/2) = (1/2) × (1/2) = 1/4 and we see that

1/4 < 1/2

4. The square of a decimal fraction less than 1 is smaller than the given decimal.

Example: 0.1 < 1 and (0.1)2 = 0.1 x 0.1 = 0.01 < 0.1.

5. A number ending in 2, 3, 7 or 8 is never a perfect square.

Example: The numbers 72, 243, 567 and 1098 end in 2, 3, 7 and 8

respectively. So, none of them is a perfect square.

6. A number ending in an odd number of zeros is never a perfect square.

Examples: The numbers 690, 87000 and 4900000 end in one zero,

three zeros and five zeros respectively. So, none of them is a

perfect square.

Many square roots are not easy to find out without using your calculator, but you can

estimate how big they are if you know a number that is smaller and a number that is larger.

Find the Square roots of:

9 49 99

9.9

First let’s look at the difference between a “square” and a “square root”: Square Square Root

Definition

Multiply number by itself.

What number, multiplied by it-self, make the

number under the symbol.

Symbol

Complete the following questions:

1) Square the following:

a) 9 b) 3 c) 1 d) 23 e) 16

2) Find each square root:

a) b) c) d) e) Use the perfect squares as a benchmark. (Ask me about the term benchmark and what it really means)

There are various techniques to find the square root of a perfect square:

1) By understanding the definition of “square root” and remembering the following:

2) Using factors to find the square root:

To find list all the factors from least to greatest:

Since the middle number doesn’t have a partner, it must multiply with itself so

Conclusion:

When a factor occurs twice, only list it once there are an _____________ number of factors. Therefore 36 is _____________________________ and the square root of 36 is _______________.

3) Using Prime factorization to find a square root:

To find make a factor tree:

We have a pair of 2’s and a pair of 3’s:

Without using a calculator, estimate each of the following and explain why you chose your

answer

a) Since 18 is not a perfect square we must estimate.

Between what two perfect squares does 18 fall between?

Extension: Caleb song buys a square mat with an area of 53 square feet. Will it fit in a

room that measures 8 feet by 10 feet? Show your work!!!!!!!!!!!!!!!!!!!!!

3. Estimate the square root of each number, to one decimal place. Check you answer with

calculator.

A) 72 b) 103 c) 55

4. Estimate each value, to the nearest one decimal place. Check you answer with calculator.

a) 14 b) 86 c) 136

5. How many whole numbers are there have a square root between 3 and 5?

In Class Work: Estimate to the nearest integer. Which integer is the closest to the square root?

21.

18 22.

62

23.

24 24.

78

25.

50 26.

98

27.

8 28.

46

Assignments: Page 99-100 Q. # 6,8,10,12,14,15 &17