Simplify Radical Expressions

What steps would you take in simplifying the following:√(3+92)

EQs… How do we simplify algebraic and numeric

expressions involving square root? How do we perform operations with square

roots?

Vocabulary Simplest Form – A radical expression is in

simplest form if no perfect square factors other than 1 are in the radicand, no fractions are in the radicand, and no radicals appear in the denominator of the fraction.

Rationalizing the Denominator – The process of eliminating a radical from an expression’s denominator.

Vocabulary Radical Conjugates –

Product Property of Radicals – States that the square root of a product equals the product of the square roots of the factors.

Quotient Property of Radicals – States that the square roots of a quotient equals the quotient of the square roots of the numerator and denominator.

baandba

00 bandawherebaab

00 bandawhereb

a

b

a

Example 1Use the product property of radicals Simplify the expression.

350

28

y

*To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

35*5 175 7*25 75

Multiply and then simplifyMultiply and then simplify

73*82 566 14*46

142*6 1412

204*52 10020 20010*20

Example 2Multiply radicals Simplify the expression.

yxy 3225

182

Example 3Use the quotient property of radicals Simplify the expression.

249

4

25

17

y

Guided Practice for Examples 1, 2, & 3 Simplify the expression.

2

5

2

123.4

45.3

3.2

72.1

x

y

x

Guided Practice for Examples 1, 2, & 3 Simplify the expression.

2

2

9

2.8

81

5.7

153.6

105.5

y

x

xyx

Example 4Rationalize the denominator

23

1

6

3

x

+To combine radicals: combine To combine radicals: combine the coefficients of like radicalsthe coefficients of like radicals

Simplify each expressionSimplify each expression

737576 78

62747365 7763

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

323502

22

212210

24*325*2

2*1632*252

Example 5Add and Subtract Radicals

202511

27633

Guided Practice for Examples 4 & 5Add and Subtract Radicals

500253.11

7310876.10

2

3.9

x

Joke of the Day… Why was the math book crying?

It had too many problems!