Class10 NCRT Real Numbers Exercise – 1.3 pdf || UP Board
Real Numbers
Exercise – 1.3
1. Prove that √5 is irrational.
Solution:
Let√5 is a rational
number.
So 5 will divide b2, Therefore 5 will divide b .…………(iii)
Now, Equations (i) and (ii) show that a and b have a common factor of 5 which is
contrary to our assumption (since a and b are co-prime numbers i.e. a and b
have no common factor other than 1.)
So this contradiction proves that contrary to our imagination, √5 is an irrational number.
2. Prove that 3+2√5 is irrational.
Solution:
Let 3+2√5 is rational
However, we know that √5 is an irrational number, So this contradiction proves that contrary to our imagination, 3+2√5 is an irrational number.
3. Prove that the following are irrationals:
(ii) 7√5
Solution:
Let 7√5 is rational
However,
we know that √5 is an irrational
number, So this contradiction proves that contrary to our imagination, 7√5 is an irrational number.
(iii) 6+√2
Solution:
Let 6+√2 is rational
However,
we know that √2 is an irrational
number, So this contradiction proves that contrary to our imagination, 6+√2 is an irrational number.
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