6.2 Evaluate Expressions with Square
Roots
Common Core Standards
8. NS.1 Know that there are numbers that are not rational, and
approximate them by rational numbers. Know that numbers that are not
rational are called irrational. Understand informally that every number
has a decimal expansion; for rational numbers show that the decimal
expansion repeats eventually, and convert a decimal expansion which
repeats eventually into a rational number.
8. NS.2 Use rational approximations of irrational numbers to compare
the size of irrational numbers, locate them approximately on a number
line diagram, and estimate the value of expressions (e.g., π 2). For
example, by truncating the decimal expansion of √2, show that √2 is
between 1 and 2, then between 1.4 and 1.5, and explain how to continue
on to get better approximations.
WARM-UP
Evaluate the expressions.
1)
5×5
3)
( −5)2
5)
25
2)
−5 × (−5)
4)
52
Evaluate Expressions with Square
Roots
Are the answers to all these expressions
the same?
7
2
7g7
(−7)2
−7g(−7)
NOTES
The square (to the second power) of both positive and
negative numbers is positive.
Concept Check
Evaluate the expressions.
6
2
15
2
( −6 )
2
( −15 )
2
NOTES
There are two square roots.
= Positive (Principal) square root
= Negative square root
= Both square roots
−
±
Examples
Evaluate the expressions.
16
− 16
± 16
− 81
± 144
EXAMPLES
Evaluate the expression.
± 400
Find the square roots of 10,000.
NOTES
To find the square root of perfect fractions (or
decimals) take the square root of both the numerator
and denominator.
Examples
Evaluate the expressions.
16
25
.16
100
−
169
− .49
EXAMPLES
Evaluate the expressions.
− .64
± .01
NOTES
To evaluate expressions with square roots always
take the square root before any other operation.
Examples
Evaluate the expressions.
36
2
121 − 2 25
4 25
− 81 + 7
EXAMPLES
Evaluate the expressions.
72
64
625 − 3 16
MORE NOTES
Some problems will have two answers because there
are two square roots.
Examples
Evaluate the expressions.
± 4 +7
± 100
2
(
9 − ± 25
)
PRACTICE
Evaluate the expressions.
± 100
1,600
5
− 49 × (−4)
144 − 2 36
± .04
7 + .25
FINAL QUESTION
Evaluate the expression.
− 25 − 8