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

Radicand – the number inside the radical sign

The number 135 is the radicand in the

expression

135

Radical Expressions

The radical sign is a symbol used to indicate a root (square root)

This expression is read“the square root of 135”

6 10

Radical Expressions

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”

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.

Simplest Radical Form

Ex 1: Express the following in simplest radical form

60 Factors of 60 include:

4 * 15

2 15

Ex 2: Express the following in simplest radical form

128

64 * 2

8 2

Ex 3: Express the following in simplest radical form

4300x

4100 * 3 * x

210 3x

Ex 4: Express the following in simplest radical form

3 450x y

2 425 * 2 * * *x x y

25 2xy x

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.