HEBREWS 11:6
And without faith it is impossible to
please him, for whoever would draw
near to God mut believe that he exists
and that he rewards whose who seek
him

LAW OF
RADICALS

LEARNING TARGETS
•Derive the laws of
radicals

9 ∙ 36
3 ∙ 6 = 18
24 ∙ 6
144 = 12

PRODUCT LAW OF RADICALS
𝑛
𝑎 ∙
𝑛
𝑎𝑏 where a and b are non-
negative when n is even, since the
square root of a negative number is
nit real number.

6𝑥 ∙ 24𝑥

3
9𝑥 ∙
3
3𝑥2

12𝑥 ∙ 3𝑥2

QUOTIENT LAW OF RADICALS
𝑛
𝑎 ÷
𝑛
𝑏 =
𝑛 𝑎
𝑏
where a and b are non-negative
when n is even and b ≠ 0. Since the square root
of a negative number is not real number; we call
this Quotient Law of Radicals.

75 ÷ 3

125𝑥4 ÷ 5𝑥2

36 ÷ 64

4
16𝑥5 ÷ 4
𝑥

HEBREWS 11:6
And without faith it is impossible to
please him, for whoever would draw
near to God mut believe that he exists
and that he rewards whose who seek
him

MATTHEW 6:15 (NIV):
“Therefore I tell you, do not worry
about your life, what you will eat or
drink; or about your body, what you
will wear. Is not life more than food,
and the Body more than clothes?”

SIMPLIFYING RADICAL
EXPRESSIONS USING
LAWS OF RADICALS

LEARNING TARGET
•Simplify radical
expressions using the
laws of radicals

72𝑦2

3𝑥
25

3
4𝑎
−8𝑏6