Download Exploring Roots

LESSON 10-3
Warm Up
Lesson 10-3 Warm-Up
ALGEBRA READINESS
LESSON 10-3
Warm Up
Lesson 10-3 Warm-Up
ALGEBRA READINESS
“Exploring Roots”
(10-3)
What is a “root”? Root: The number that tells you how many times the base is multiplied by itself
to equal a given number. The roots is shown in front of the radical sign (called
the radicand). If there isn’t a number in front of the radical, the root is “2”.
Example:
144 is the “square root of 144” (Since 12 x 12 = 144, 144
= 12)
Rule: Roots: For any real numbers a and b and n ≥ 0, if an = b, then a is the
nth root of b.
How can you
read a radical?
Recall that
sign means “the square root of” (or what times itself equals
the number in the radicand). Therefore,
means “the cubed root of” (or what
times itself three times equals the number in the radicand),
means “the
fourth root of” (or what times itself four times equals the number in the
radicand), and so on.
Examples:
ALGEBRA READINESS
“Exploring Roots”
(10-3)
How do you find
the root of a
number?
To find the root of a number, think of a number that when multiplied by itself n
time (the power of the root, which is in front of the radical sign), it equals the
number in the radicand.
Note: There are always two solutions of an even nth root (like square root, fourth
root, sixth root….), because a negative times a negative is a positive . There is
only always one solution of an odd nth root (like cubed root, fifth root, seventh
root….), because a positive times a negative is a always a negative.
Example: Find two square roots of 81.
Example:
ALGEBRA READINESS
Exploring Roots
LESSON 10-3
Additional Examples
Simplify 3√–64 .
Because –64 is negative, the cube root is also negative.
(–4)3
= (–4) • (–4) • (–4) = –64
Find the number that,
when multiplied by itself
three times, equals –64.
So 3√–64 = –4.
ALGEBRA READINESS
“Exploring Roots”
(10-3)
How do you
A radical is a grouping sign, so when you simplify an expression using the order
simplify an
of operations (PEDMAS), radicals are the same as the “P” for parenthesis. In
expression with a other words, simplify under the radical sign (radicand) first.
root?
Example:
ALGEBRA READINESS
Exploring Roots
LESSON 10-3
Additional Examples
Simplify 3 + 2 • √ 50 – 14
3 + 2 • √ 50 – 14
= 3 + 2 • √36
Work inside grouping symbols.
= 3 + 2 • ±6
Simplify the root.
= 3 + (±12)
Multiply.
= 15 or -9
Add.
ALGEBRA READINESS
Exploring Roots
LESSON 10-3
Lesson Quiz
Simplify each expression.
1. √ 225
15
2. 3√ –27
–3
3. 4 • 3√ 90 + 5 • 7
4. √ 36 + 45 – 8
20
1
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