SECTION 10.3
Multiply radical expressions.
√4 ∙ √25 =
Product Rule for Radicals
𝑛
√100 =
𝑛
If both √𝑎 and √𝑏 are real numbers, then ___________· ___________ = _____________________.
The _______________ (root) must be the _______________!!!
Multiply:
√3 ∙ √12 =
√5 ∙ √7 =
3
√3𝑎 ∙ √5𝑏 =
Divide radical expressions.
16
�
25
√16
=
Quotient Rule for Radicals
𝑛
3
�𝑥𝑦 ∙ √7𝑥 =
√25
=
𝑛
If both √𝑎 and √𝑏 are real numbers, then
=
The _______________ (root) must be the _______________!!!
, where 𝑏 ≠ 0.
Divide:
√49
√64
=
√243
√3
=
√15
√81
√21
√3
=
=
Use the product rule to simplify radical expressions.
Simplify radicals:
Look for the _______________ perfect square that _______________ into the _____________ evenly.
√20
√75
√60
√48
Simplify radicals:
_______________ a factor __________.
√9 = √
=
The tower works because of the definition of what a square root is. The square root of 9 is 3 because
we have two of the same factor underneath the radical. Because we’re doing square roots, for every
two of the same factor, we can bring one to the outside.
√20 = 2√5
√20 = √
Divide by _______________ numbers!! 2, 3, 5, 7, 11, …
√60 = 2√15
√60 = √
√48 = 4√3
√48 = √
Simplify radicals:
√245
√300
√52
√108
Simplify.
√486
Simplify radicals.
√𝑥 3
Simplify:
�75𝑥 7 𝑦 3
Simplify:
√48𝑎3 𝑏 7 𝑐 4
Simplify radicals:
Simplify:
3
3
√250
�24𝑥 7 𝑦 2 𝑧 5
√𝑥 5
√𝑥 9
3
√243
Simplify:
Simplify:
Simplify:
6√15𝑐 2 ∙ 2√10𝑐 5
54√240𝑟 9 𝑠 10
9√5𝑟 6 𝑠 4
√3𝑚2 √9𝑚3
Do you have any questions in regards to Section 10.3 video and homework?