Multiplying Radicals: Simplify and Multiply Expressions
Simplify expressions involving variables and numbers, multiply radicals using the distributive property, find missing terms, and rationalize denominators. Practice examples with step-by-step solutions provided throughout. Learn to multiply various radical expressions and find conjugates for complex numbers.
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Presentation Transcript
Check up Simplify the following: 75x 1) 8x 10y 2)
Check up 2 Simplify completely, if possible. -4 7 3 3 9 7 3) 50xy 2 2 4)
Chapter 7 Section 5 Multiplying Radical Expressions with More Than One Term Page 542
Multiplying Radicals Use the distributive property and multiply ( ) 7 x+ 2 a) b) 4(x + 2) ( ) +7? 4 3 3 3 3 6 c)
Multiply ( )9-4 5 ( ) 5x+4 ( ( ( )3x-2 ( ) 6+ 5 a) b) )2 2+5 3 ( ) 3 2-4 3 c) ) ( 2 2- 7 d) e) ( ) ) 2- 7 2+ 7
Find the missing term 6 ? ( )=6 ? ( )=2 3y ? ( )=3y 1) 2) 3 2 3)
Rationalize the Denominator Process that involves rewriting a radical expression as an equivalent expression in which the denominator no longer contains any radical.
Rationalize the Denominator 5 6 Solution: What value does one multiply the denominator, so the radical disappears? 6 ? ( )=6 6 6 6 (?) = , so multiply the fraction by a form of one 6
Rationalize the Denominator Solution: 5 6 5 6 6 6 30 6
Rationalize the Denominator What value of one do you multiply the fraction to rationalize the denominator? 7 3 1) 10 2) Be careful 5 9 3x2y 3 3)
Rationalize the Denominator 3 2 1) 4 2) 3 x 3)
Conjugate Find the conjugate for the following: 2- 7 a) 6-4 7 b) 3 6+ 5 c)
Rationalize the Denominator If the denominator contains two term, multiply the numerator and denominator by the conjugate of the denominator.
Rationalize the Denominator 4 Denominator contains two terms. 3 2+4 Find the conjugate of the denominator, 3 2 4 Multiply the numerator and denominator by the conjugate. 3 2-4 3 2-4 ) )3 2-4 4 3 2+4 ( 4 3 2-4 ( ( ) 3 2+4
Continue ( ) 4 3 2-4 )3 2-4 ( 3 4-16 ( ( ( ) 3 2+4 ) ) Simplify 4 3 2-4 4 3 2-4 -? 4 -? 3 2+4 Reduce:
Problem Rationalize the denominator: 11-5 11+5 What is the conjugate of the denominator? What do you do with the conjugate?
Try Rationalize the denominator 15 6+1 1) x +1 x +3 2)
Summary Multiply radicals One term many terms Two terms two terms Two terms squared Conjugate Rationalize the denominator
