prove that √2-√5 is an irrational number. in step by explanation.
Answers
Step-by-step explanation:
search-icon-header
Search for questions & chapters
search-icon-image
Class 10
>>Maths
>>Real Numbers
>>Revisiting Irrational Numbers
>>Prove that 2 + √(5) is an irrational num
Question
Bookmark
Prove that 2+
5
is an irrational number.
Easy
Solution
verified
Verified by Toppr
If possible, let us assume 2+
5
is a rational number.
2+
5
=
q
p
where p,q∈z,q
=0
2−
q
p
=−
5
q
2q−p
=−
5
⇒−
5
is a rational number
∵
q
2q−p
is a rational number
But −
5
is not a rational number.
∴ Our supposition 2+
5
is a rational number is wrong.
⇒2+
5
is an irrational number
Answer:
If possible, let us assume 2+
5
is a rational number.
2+
5
=
q
p
where p,q∈z,q
=0
2−
q
p
=−
5
q
2q−p
=−
5
⇒−
5
is a rational number
∵
q
2q−p
is a rational number
But −
5
is not a rational number.
∴ Our supposition 2+
5
is a rational number is wrong.
⇒2+
5
is an irrational number.