How are Exponents related to Radicals?

HOW ARE EXPONENTS RELATED TO RADICALS?

a1n= n√a

VOCABULARYRadical SignRadical Expression

An expression that contains a radical sign.

Index A small number indicating the root or a radical expression

Radicand The number inside a radical sign 

Prime Number

A Prime Number can be divided evenly only by 1, or itself. And it must be a whole number greater than 1.

Factor Factors are numbers you can multiply together to get another number

Prime Factor

A factor that is a prime number

Prime Factorization

Finding the prime numbers that multiply together to make the original number.

IDENTIFY THE RADICAND & INDEX FOR THE FOLLOWING EXPRESSIONS.

Radicand:

Index:

Radicand:

Index:

Radicand:

Index:

SIMPLIFYING RADICALS WITH PRIME FACTORIZATION

Prime Factorizatio

n360

SIMPLIFYING RADICALS WITH PRIME FACTORIZATION

Prime Factorizatio

n243

SIMPLIFYING RADICALS WITH PRIME FACTORIZATION

Prime Factorizatio

n75

COMBINING LIKE RADICALSWe can add or subtract like radical expressions by adding or subtracting the coefficients. (Like radicals have the same index and radicand)

When adding or subtracting like radicals, the radicand does

not change.

EXAMPLE 1: SIMPLIFY EXAMPLE 2: SIMPLIFY

11√5+4 √58 √10+ 5√4−2√10+7 5√ 4

QUICK CHECK TIME!!

Get out

your

white

boards!!

SIMPLIFY

√12

SIMPLIFY

√50

SIMPLIFY

√ 45

SIMPLIFY

2√18

SIMPLIFY

8 √28

SIMPLIFY

−3 √1000

SIMPLIFY

√16𝑛2

SIMPLIFY

√20𝑛2

SIMPLIFY

√ 49𝑛3

SIMPLIFY

√25 𝑥2𝑦

SIMPLIFY

√90 𝑥4 𝑦 2

SIMPLIFY

√81 𝑥3 𝑦 2