NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No.2 Solutions : Prove that 3 + 2 √5 is irrational.
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CBSE/NCERT MATHS Class 10 Ex- 1.3 Q No.2 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. 2 : Prove that 3 + 2 √5 is irrational.
Let 3 + 2 √5 is rational .
Therefore , we can find two co-prime integers a, b (b≠0) such that
3 + 2 √5 = p/q
= 2 √5 = p/q -3
= √5 =1/2 ( a/b – 3)
Since a and b are integers, 1/2 ( a/b – 3) will also be rational and therefore, √5 is rational. This contradicts the fact that √5 is irrational. Hence, our assumption that 3 +2 √5 is rational is false. Therefore, 3 + 2 √5 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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