Simplifying Radicals and Imaginary Numbers

Simplify radicals

• Learning Target:

•I can fluently simplify radicals with variables.

• Vocabulary:

•
Exponent

•
Root

•
Rational Exponent

•
Radical -nth root

•
Rational exponent

• Check, name the following part of a radical

• 1. Name 8:
• 2. Name 8a^3:
• 3. Which number represent the exponent?
• 4. Name the index :
• 5. when there is not an index, we assume it is:

Multiple Choice

Name 8

• coefficient

• radical

• radicand

• exponent

Multiple Choice

Name 3

• coefficient

• radical

• radicand

• exponent

Multiple Choice

Name 8a^3

• coefficient

• radical

• radicand

• exponent

Multiple Choice

Name the index

• 3

• 2

• 8

• 1

Steps to simplify radicals with variables

• 1. If there is a coefficient, simply first. You can use

a calculator.

• 2. For the variable, divide the exponent by the

index.

• 3. The quotient will the exponent of answer.
• 4. If there is a remainder, keep the remainder

inside of the radical.

Examples:

Multiple Choice

simplify

• a^18

• a^10

• a^22

• a^3

Multiple Choice

simplify

• x^5y^3

• xy

• xy^16

• x^16

Multiple Choice

simplify

• x^5y^3z

• xyz

• x^2y^2z^8

• xy^2z^4

• Check-point, simplify:

What if the exponent of the radicand is not an
even number

• Check-point ,simplify the radicals

Open Ended

simplify

Open Ended

simplify

Open Ended

simplify

Simplify radicals that the index is not 2 .

• Check-point, simplify the radicals

Multiple Choice

simplify

• x^9

• x^15

• x^4

• x

• Simplify a radical with coefficient and variables

• Check-point, simplify radicals

Multiple Choice

• x

• 10x^3

• 25x^3

• 5x^3

"i" is known as the imaginary unit,
or unit imaginary number, and is
defined as the square root of -1.

Quiz

• https://quizizz.com/admin/quiz/6245f86f72729b001d30382b?sou

rce=quiz_share

Closure:

• Quick write, in a couple sentences explain how would
you simplify a radical with variables?