1.2 Square Roots of Non-Perfect Squares
-A fraction or decimal that is not a Perfect Square is
called a NON-PERFECT SQUARE. That is, they
cannot be written as a product of 2 equal fractions.
Ex. of Non-Perfect Square =
75
10
to check it, square root numerator and/or
denominator and check if they are perfect
squares! If just one of the numbers IS NOT a
perfect square, then it's a Non-Perfect Square.
A 5 m ladder is placed against
a wall. The base of the
ladder is 1.5 m from the wall.
How far up the wall does the
ladder reach?
5m
1.5 m
What happens when you try to find the square root if 5.5 on
your calculator?
√5.5 = ?
To find the square root of a non-perfect square, we can
benchmark, estimate, or use a calculator!
Benchmarking
√27 = ?
i) √50
Estimating
√
10 = ?
26
ii) √8
5
Calculator
√0.38 = ?
iii) √12.8
The Pythagorean Theorem often
involves non-perfect squares:
c
a2 + b2 = c2
b
a
18 cm
h
14 cm
Steps:
1. Identify the hypotenuse.
2. Replace known variables.
3. Solve for the unknown using your
mad square root skills!
Find the value of the unknown side:
x
2m
4 mm
h
2.7 mm
14 cm
6 cm
x
Ex. 3 P. 17
1.5m
2.2m
6.5m
The sloping face of this ramp needs to be covered in carpet.
Calculate the area of carpet needed.
Which of the following are perfect squares?
P.S.
Non P. S.
110
16
81
36
4.12
49
16
6.25
17
2.89
1
20
49
Practice P. 18-20
Numbers: 6ab,7ac, 9ac, 10abd, 13ac, 16, 19ab