 ## Presentation on theme: "Simplifying Radicals."— Presentation transcript:

Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 196 49 625

How do you simplify variables in the radical?
Look at these examples and try to find the pattern… What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

X

Simplify = = = This is a piece of cake! = =

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

Simplify each expression

Simplify each expression

Simplify each expression: Simplify each radical first and then combine.

Simplify each expression: Simplify each radical first and then combine.

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

Simplify each expression

Simplify each expression

WORKSHEET 3)

5) 7)

9)

11)

13)

15)

17)

Multiply and then simplify

WORKSHEET(MULT)

WORKSHEET(MULT)

WORKSHEET(MULT)

WORKSHEET(MULT)

WORKSHEET(MULT)

WORKSHEET(MULT)

Using distributive Property
a(b+c) = ab + ac a(b-c) = ab - ac

USING THE DISTRIBUTIVE PROPERTY

USING THE DISTRIBUTIVE PROPERTY

USING THE DISTRIBUTIVE PROPERTY

USING THE DISTRIBUTIVE PROPERTY

USING THE DISTRIBUTIVE PROPERTY

USING THE DISTRIBUTIVE PROPERTY

USING THE DISTRIBUTIVE PROPERTY

USING THE DISTRIBUTIVE PROPERTY

Using the FOIL

Using the FOIL

Using the FOIL

Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

That was easy!

42 cannot be simplified, so we are finished.
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

This can be divided which leaves the radical in the denominator
This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

This cannot be divided which leaves the radical in the denominator
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

This cannot be divided which leaves the radical in the denominator
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

How do you simplify variables in the radical?
Look at these examples and try to find the pattern… What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

How do you simplify variables in the radical?
Look at these examples and try to find the pattern… As a general rule, divide the exponent by two.

Simplify = = = = =

Simplify = = = = =

Simplify = = = =

= = ? = =