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Byju's Answer
Standard X
Mathematics
Irrational Numbers
Prove that 2+...
Question
Prove that
2
+
3
is an irrational number, given that
3
is an irrational number.
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Solution
Let us assume that
2
+
3
is a rational number.
Thus,
2
+
3
can be represented in the form of
p
q
,
where p and q are integers, q ≠ 0, p and q are co-prime numbers.
2
+
3
=
p
q
⇒
3
=
p
q
-
2
⇒
3
=
p
-
2
q
q
Since
,
p
-
2
q
q
is
rational
⇒
3
is
rational
But
,
it
is
given
that
3
is
an
irrational
number
.
Therefore
,
our
assumption
is
wrong
.
Hence
,
2
+
3
is
an
irrational
number
.
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