Post on 22-Feb-2016
description
Substituting Surds
Slideshow 18 Mathematics
Mr Sasaki Room 307
Objectives
▪Substitute surd expressions into algebraic expressions▪Rationalise surd denominators when substituting
Substitution
As we have known for a long time now, substitution is the process of inserting expressions into other expressions.We’ve substituted numerical expressions and algebraic expressions. Today we will substitute surd expressions. The process is similar.
Surd SubstitutionIn a simple case, we just need to substitute and then simplify the expression.ExampleIf and , calculate .
𝑎2𝑏+2=¿(3 √2 )2 ∙2√3+2¿18 ∙2√3+2¿36 √3+2
Try the first worksheet!
Answers - Easy
2√14 6 √2 7± 4 4√14+4 8 √7−356 64 2√2
18 4√5+21 6 √10+3√2−1−4 √5−3 36 36 √5+18±6 √5±1020
Answers - Hard
√2+1 1 2√2+22√2 4 4√2+8√2+1 1 1
−4 6 √5+14−214 √5+30 6 √5+10 −64 √5−192√5+2√2+3 3√5+3−2√5−18
Other CasesLet’s recall a few properties about indices.
𝑥− 1≡1𝑥1
𝑥12
≡√𝑥𝑥
𝑥− 𝑦≡1𝑥 𝑦
ExampleIf , calculate .𝑥− 1=¿
1𝑥=¿
1√8
=¿12√2
=¿√2
2√2 ∙√2
¿ √24
Other CasesLet’s try a harder example.ExampleIf and , calculate . Only consider the positive root.
2𝑥−2𝑦 =¿ 2
𝑥2 𝑦=¿
2(√8+1)2 ∙3√2
=¿ 2(4√2+9)∙3√2
¿2
27√2+24¿ 227√2+24
∙ 27 √2−2427 √2−24¿
2 (27√2−24 )(27√2 )2−242
¿ 54 √2−481458−576
¿ 54√2−48882
¿ 9√2−8147
Answers - Easy√22 2√28
112
√22 √218
3−√27
√2+3 √2−13
4−6 √2 √77
Answers - Hard
√2+1 2√2+349
2√2+3 −17√2+7 8 √42+12√21111
13−4√3112√3 3+√11
11 13−4√3√1111 11√11