Transcript Objective 123 – Simplify square roots

Aim: How do we simplify
radical expressions?
Do Now: List at least 3 factors of:
60
128
300x4
Do Now: List at least 3 factors of:
60
128
300x4
Radical Expressions
135
The radical sign is a
symbol used to indicate
a root (square root)
This expression is read
“the square root of 135”
Radicand – the number
inside the radical sign
The number 135 is the
radicand in the
expression
Radical Expressions
6 10
The number 6 is outside the radical
sign and should be multiplied against
the square root
This expression is read
“Six times the square root of ten”
Simplest Radical Form
A radical expression is in simplest form when:



No radicands have perfect square factors
other than 1.
No radicands contain fractions.
No radicals appear in the denominator of a
fraction.
Ex 1:
Express the following in simplest
radical form
60
4 * 15
2 15
Factors of 60 include:
Ex 2:
Express the following in simplest
radical form
128
64 *
2
8 2
Ex 3:
Express the following in simplest
radical form
300 x
100 *
10 x
4
3*
2
3
x
4
Ex 4:
Express the following in simplest
radical form
3
50 x y
25 *
5 xy
4
2*
2
2x
2
x *
x*
y
4
Ex 5:
Express the following in simplest
radical form
2744
14 14
Simplify by using
multiple steps
Simplifying Radical Expressions
1) Analyze factors of the radicand
2) Find the largest perfect square factor
3) Divide the radicand into two or more radical
expressions
4) Take the square root of all perfect square
radicands (half all even exponents)
5) Multiply all factors outside the radical signs
Multiply all of the factors inside the radical
signs.