NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No.1 Solutions : Prove that √5 is irrational
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CBSE/NCERT MATHS Class 10 Ex- 1.3 Q No.1 Solutions
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Real Numbers CHAPTER : 1
Symbol of real numbers (ℝ) In mathematics, the real number is the value presented to any amount corresponding to the simple line. Actual numbers include all rational numbers such as -5 and fractional numbers such as 4/3 and all irrational numbers such as √2 (1.41421356 …, square root of 2, an unregulated algebraic number). By incorporating the ample numbers in the actual numbers, they can be presented from the eternal points that can be attributed on a line in the form of a real number line.
Exercise- 1.3 Question No. 1 : Prove that √5 is irrational
Let √5 is a rational number.
Therefore, we can find two integers a, b (b≠0) such = √5 = a/b Let a and b have a common factor other than 1. Then we can divide them by the common factor, and assume that a and b are co- prime.
a = b
a2 = 5b2
Therefore, a2 is divisible by 5 and it can be said that a is divisible by 5.
Let a = 5k, where k is an integer
(5k)2 = 5b2
5k2 = b2
This means that b2 is divisible by 5 and hence, b is divisible by 5. This implies that a and b have 5 as a common factor. And this is a contradiction to the fact that a and b are co-prime. Hence, √5 cannot be expresswed as p/q or it can be said that √5 is irrational .
CLICK ON RED BOX FOR CBSE Maths Class 10 Exercise 1.3 Real Numbers Next Question Answer :-
SEE NCERT Maths Class 10 Chapter 1 Ex-1.3 All Questions Solutions
- NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No.1 Solutions : Prove that √5 is irrational
- NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No. 2 Solutions : Prove that 3 + 2 √5 is irrational.
- NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No. 3 Solutions : Question 3 : Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2
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