simplify radical expressions what steps would you take in simplifying the following: (3+9 2 )
TRANSCRIPT
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!