NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No.3 Solutions : Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2
Hy Friends Welcome On NCERT MATHS SOLUTIONS !! Today we are going to solve the Question : ”Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2 ” of Exercise 1.3 Question No 2 Solutions (Real Numbers) of Class 10th, which will prove to be very helpful for you.
CBSE/NCERT MATHS Class 10 Ex- 1.3 Q No.3 Solutions
If you are a student of CBSE, today we are going to give you the CBSE / NCERT Chapter : Real Numbers Exercise 1.3 Question No – 3 Solutions . Hope you like this post about Class 10th Maths Solution.
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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 the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2
Let 1/√2 is rational .
Therefore, we can find two co-prime integers a, ba (b ≠ 0) such that
Or 1/√2 = a/b
√2 = a/b
b/a is rational as a and b are integers.
Therefore, √2 is rational which contradicts to the fact that √2 is irrational.
Hence, our assumption in false and 1/√2 is irrational.
Let 7√5 is rational.
Therefore, we can find two co-prime integers a, b (b ≠ 0 ) such that
7√5 = a/b
= √5 = a/7b
a/7b is rational as a and b are integers.
Therefore, √5 should be rational. This contradicts the fact that √5 is irrational.
Therefore, our assumption that 7√5 is rational is false. Hence, 7√5 is irrational.
(iii) 6 + √2
Let ) 6 + √2 be rational.
Therefore, we can find two co-prime integers a, ( b ≠ 0 ) such that
6 + √2 = a/b
√2 = a/b – 6
Since a and b are integers, a/b-6 is also rational and hence, √2 should be rational. This contradicts the fact that√2 is irrational. Therefore, our assumption is false and hence, 6 + √2 is irrational.
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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