Download Math 9 Unit 1 Lesson 1.2 Square Roots of Non

Math 9 Unit 1
Lesson 1.2 Square Roots of Non-Perfect Squares
Perfect Squares:
Recall that a perfect square (square number) is a number that is formed by squaring a
number (that is, multiplying a number by itself)
Eg.
Eg.
5 = 5 × 5 = 25, so 25 is a perfect square
0.3 = 0.3 × 0.3 = 0.09, so 0.09 is perfect square
Perfect squares can be written as the product of two identical numbers.
Eg.
36 = 6 × 6
Eg.
= ×
Square Roots of Perfect Squares:
The square root of a perfect square, written in decimal form, is a terminating or
repeating decimal.
Note: a terminating decimal stops, for example 0.4, 1.75, 23.05468
,
Note: a repeating decimal has repeating digits, for example 0.33333… , 4. 27
72.165165165…
A number that is not a perfect square is called a non-perfect square.
The square root of a non-perfect square, written in decimal form, is a non-terminating,
non-repeating decimal.
Estimating Square Roots of Non-perfect Squares:
Example 1: Estimate each square root using Perfect Squares as Benchmarks.
A. 0.9
B. 14.6
Example 2: Estimate each square root using Perfect Squares as Benchmarks.
A. B. Note: Converting the fractions to the closest perfect square may not produce a
reasonable approximation. Converting to a decimal may produce a more accurate
approximation.
Example 3: Estimate each square root using your calculator.
A. 5.2
B. Applications of square roots:
Square roots can be used to calculate lengths of the sides of a triangle using the
Pythagorean Theorem.
Practice: Page 18 -20 # 6ad, 7ade, 9, 11adeh, 13ad, 16, 17