Lesson Plan – Simplifying Square Roots
Objective: To allow students to develop a better understanding of square roots and how
to simplify them. Students will learn the multiplication property of square roots.
Grade Level: 8th, Geometry, Algebra
Standards: SOLs: G.8, A.3
(http://www.doe.virginia.gov/VDOE/Superintendent/Sols/home.shtml)
NCTM: Students will understand square roots and how to simplify them to solve problems.
(http://standards.nctm.org/document/chapter7/index.htm).
Materials: Notes
White board
Procedure:
1. First have the students list the first ten perfect squares:
a. 12=1, 22=4, 32=9, 42=16, 52=25, 62=36, 72=49, 82=64, 92=81, 102=100
2. Discuss why these are perfect squares.
3. Define what a perfect square is: If b2 = a, then b is the square root of a. Further if
b*b = a, then b is the square root of a.
4. Example problems to do as a class: (Note: in the discussion make sure students
understand that when you multiply square roots you can combine them under one
square root!)
a. √(12) = √(4*3) = √(4)*√(3) = 2*√(3)
√(48) = √(16*3) = √(16)*√(3) = 4*√(3)
√(102) = √(102)
√(24) = √(4*6) = √(4)*√(6) = 2*√(6)
√3*√6 = √18 = √9*2 = √9*√2 = 3*√2
(If time allows – combine with distributive property)
√(2)*(6+√12) = √2*6+√2*√12 = 6*√2 + √24 = 6*√2 + √24*6
5. Why is 6*√ (18) not in simplest radical form?
6. Discuss the difference between the √ (9) and √ (-9)
7. Why can’t we take the square root of a negative number?
a. Because a negative*negative is a positive and a positive*positive is a
positive. So no number times its self can be negative.
Possible Problems:
b.
c.
d.
e.
f.
1.
Students may not be able to find the factors. In this case I could show them how
you could test all of the perfect squares.
2. Students may not understand why you can split up the numbers into factors. In
this case I would show them how the factors can multiply and it is still the same
number, just written a different way. Then I could show them how the number
outside the radical is still multiplied just like the factors so it does not change the
value.
Sources:
"Standards for Grades 9 - 12." Principles & Standards for School Mathematics. 2004.
National Council of Teachers of Mathematics. 21 Feb 2009
<http://standards.nctm.org/document/chapter7/index.htm>.
"Standards of Learning Currently in Effect ." Standards of Learning. Virginia Department
of Education. 21 Feb 2009
<http://www.doe.virginia.gov/VDOE/Superintendent/Sols/home.shtml>.