Algebraic Operations Root Shape

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MATH




Andrea Fauzian

, ALGEBRAIC OPERATIONS ROOT SHAPE


1. Definition of the Root shape
If a is a real number as well as m, n are positive integers, then it applies:
1
a) a n = n a
m
n
b) a n = a m


2. Root Form Algebra Operations
For every positive number a, b, and c the relationship applies:
a) a c + b c = (a + b) c
b) a c – b c = (a – b) c
c) a b = ab

d) a+ b = (a + b) + 2 ab

e) a− b = (a + b) − 2 ab


3. Rationalizing the denominator
For every fraction whose denominator contains irrational numbers (numbers that cannot
be rooted), the denominator can be rationalized by the following rules:
a) a
= a  b =a b
b b b b

c( a − b )
b) c
= c
 a− b =
a+ b a+ b a− b a −b

c(a − b )
c) c
= c
 a− b = 2
a+ b a+ b a− b a −b




QUESTION DISCUSSION

2√7
1. Simple form of =… 2√7 2√7 √5−√2
√2 +√5 = ×
2 2
A. √35 − 3 √10 √2 +√5 √5+√2 √5−√2
3
2 2√7(√5−√2)
B. 3 √35 − √5 =
5−2
2 2
C.
3
√35 − 3 √14