Download Honors Math 2 Name: Definition and Properties of Square Roots

Honors Math 2
Definition and Properties of Square Roots
(Sections 1.02-1.04)
Definition:
If r ≥ 0 , the square root
1. s ≥ 0
2. s2 = r
Name:
Date:
r is a real number s such that:
€
(NOTE:€Your textbook sometimes
calls this the “Duck Principle”)
€
€ nonnegative real number has exactly one square root.
Postulate:
Every
Examples:
Use the definition of a square root to prove
49 = 7 .
€
Use the definition of a square root to prove
5=
10
.
2
€
Is the conjecture
x 2 = x true for all real numbers x?
€
Theorem:
If x and y are nonnegative numbers, then
Proof:
€
x⋅
y = xy .
Theorem:
If a and b are nonnegative numbers with b ≠ 0 , then
a
a
=
.
b
b
Proof:
€
Is the conjecture
€
a + b = a + b true for all nonnegative numbers a and b?
€
Conventions for Square Roots
• Simplify all square roots – replace perfect squares inside the square root sign with
their square roots outside the square root sign.
• Do not leave a square root sign in the denominator.
Examples:
50
€
1
3
€
48 − 3
€
For You to Do
1. Simplify the expression by combining like terms.
3 2 − 6 5 − 1.25 2 − 2 17 + 8 5 + 1.25 2 + 2 6 + 6
2. Write each square root in simplified form by finding perfect squares in the number
under the
symbol.
32
92
20
1800
3. Write each fraction in simplified form by eliminating the square root in the
denominator.
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Homework: page 10 #2, 8
page 14 #1, 2, 5, 6
page 18 #2, 5, 6
(Reminder: When textbook says “Duck Principle,” it means the definition of square root)