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Byju's Answer
Standard IX
Mathematics
Real Numbers
Give an examp...
Question
Give an example of two irrational numbers, whose
product is an irrational number.
A
√
3
,
√
3
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B
√
2
,
√
2
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C
√
2
,
−
√
2
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D
√
2
,
√
3
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Solution
The correct option is
D
√
2
,
√
3
Consider option
A
.
The number are
√
3
and
√
3
.
Their product
=
√
3
×
√
3
=
3
, which is a rational number.
Consider option
B
.
The number are
√
2
and
√
2
.
Their product
=
√
2
×
√
2
=
2
, which is a rational number.
Consider option
C
.
The number are
√
2
and
−
√
2
.
Their product
=
(
√
2
)
×
(
−
√
2
)
=
−
2
, which is a rational number.
Consider option
D
.
The number are
√
2
and
√
3
Their product
=
√
2
×
(
√
3
)
=
√
6
, which is an irrational number.
Therefore, option
D
is correct.
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Similar questions
Q.
check whether the following statement is True or False:
The product of these two irrational numbers
√
3
+
3
√
2
and
√
2
−
√
3
is also an irrational number.
Q.
Give an example of two irrational numbers, whose
product is a rational number.
Q.
The pair of irrational numbers whose product is rational are
2
√
3
−
3
√
2
and
2
√
3
+
3
√
2
Q.
Give an example of a number x such that x
2
is an irrational number and x
3
is a rational number.
Q.
Give an example of two irrational numbers, whose
sum is an irrational number.
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