6. Give an example of two irrational numbers whose
(i) difference is an irrational number.
(ii) difference is a rational number
(iii) sum is an irrational number.
(iv) sum is a rational number.
(v) product is an irrational number.
(vi) product is a rational number.
(vii) quotient is an irrational number.
(vin) quotient is a rational number.
Answers
Answer:
) Consider the two irrational number 2+
3
and
3
−2.
Their sum =2+
3
+
3
−2=2
3
is an irrational number.
(ii) Consider the two irrational numbers
2
and −
2
.
Their sum =
2
+(−
2
)=0 is a rational number.
(iii) Consider the two irrational numbers
3
and
2
.
Their difference=
3
−
2
is an irrational number.
(iv) Consider the two irrational numbers 5+
3
and
3
−5.
Their difference =(5+
3
)−(
3
−5)=10 is a rational number.
(v) Consider the two irrational numbers
3
and
5
.
Their product =
3
×
5
=
15
is an irrational number.
(vi) Consider the two irrational numbers
18
and
2
.
Their product =
18
×
2
=
36
=6 is a rational number.
(vii) Consider the two irrational numbers
15
and
3
.
Their quotient =
3
15
=
3
15
=
5
is an irrational number.
(viii) Consider the two irrational numbers
75
and
3
.
Their quotient =
3
75
=
3
75
=5 is a rational number.
PLEASE FOLLOW ME
Answer:
2 + √5 , and 3 + √5
ii) 10 + 3 , 5 - √3
iii) 3 +√2 , 3 - √2
iv) 5√3 , 3√3
v) 3 - √5 , 5 +√3
vi) 5 √8 , √2
vii) 2√3 , √3
viii) 2√10 , 2√2