Homework Solution lesson 8.5

9) X = 12

10)

11) n = 0

12) M = -3

13) Z = 8

14) T = 5

Homework

Lesson 8.7_page 533

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Lesson 8.7 Simplifying Radical Expressions

Properties of Radicals

For any real number a,

EXAMPLE:

Examples

√ 49𝑥2 𝑦5𝑚6Answer:

STRUCTURE

You can write an expression with rational exponent in radical form

Rewrite each expression in radical form

Radicals - definitions

The definition of is the number that when multiplied by itself 2 times is x.

x

2224 xxxx 2

16 8

Simplifying radicals

Most numbers are not perfect squares, but may have a factor(s) that is (are) a perfect square(s).

The perfect squares are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

Simplify the radical expression by factoring out as many perfect squares as possible:

Simplifying radicals

The perfect cubes are:

1, 8, 27, 64, 125,…

Simplify the radical expression by factoring out as many perfect squares as possible:

Try these - simplify:

If a radical has a perfect square factor, then we can pull it out from under the sign.

Ex:

98724832

50 22525 25

745 bax

Warm-Up # Solve the equation by using the LCD. Check for

extraneous solutions.

Simplify

𝟐 𝒙𝒙+𝟑

−𝟏=𝒙

𝒙+𝟑

98

323

Homework Solution lesson 8.7

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Homework

Lesson 8.7 page 534

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Lesson 8.7

Adding, Subtracting, and Multiplying Radical Expressions

Combining like-terms

3x+2x – 2

(3+x) + (3 + x)

(4 + n) –(-1 -3x)

Adding or Subtracting Radicals

24232

24232182

To add or subtract square roots you must have like radicands (the number under the radical).

Sometimes you must simplify first:

TRY THESE:

5553

48753

)241()183(

)2431()66(

Multiplying Radicals

62343232

10152553

You can multiply any square roots together. Multiply any whole numbers together and then multiply the numbers under the radical and reduce.

TRY THESE:

10253

2261

)32)(123(

2

52

Warm-Up #

Simplify

Homework Solution lesson 8.7

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Homework

Lesson 8.7 page 533

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#82-84 ALL

Lesson 8.7

Dividing and Rationalizing Radical Expressions

Dividing RadicalsTo divide square roots, divide any whole numbers and then divide the radicals one of two ways:

1) divide the numbers under the radical sign and then take the root, OR

2) take the root and then divide. Be sure to simplify.

5

20

5

20 2

5

52

5

20 24

5

20 or

YOU TRY

4

110

40

4

10022

148

25

100

10

80

Converting Back and Forth

Convert from exponential to radical form:

Converting from radical to exponential:

Example

(64 𝑦7)13

3√𝑦 3

Rationalizing Radicals It is good practice to eliminate radicals from the denominator of

an expression. For example:

We do not want to change the value of the expression, so we need to multiply the fraction by 1. But “1” can be written in many ways…

2

3 2

222 2

21

2

23

22

23

2

2

2

3

We need to eliminate

Since we will multiply by one where

YOU TRY

3

5

15

2

10

53

23

35

83

52

120

72