Exercise 1.3: Irrational Numbers
Here you'll prove that numbers like √2 and √3 are irrational using proof by contradiction. These proofs are a favourite in board exams — understanding the logic is key.
Extra Practice Questions
These questions cover the same concepts as Exercise 1.3. Try solving them to build confidence before or after the textbook exercise.
If the HCF of 408 and 1032 is expressible in the form 1032p - 408 x 5, find p.
If n is any natural number, can 6^n end with the digit 0?
Which of these has a terminating decimal expansion?
The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, find the other.
Using Euclid's division algorithm, the HCF of 455 and 42 starts with which division?
Prove that sqrt(2) + sqrt(3) is irrational. If we assume it's rational (= a/b), what do we get when we square both sides?
Which of the following is a rational number?
Use Euclid's division lemma to show that the square of any positive integer is of the form 3m or 3m+1.
The HCF of 96 and 404 using Euclid's algorithm is:
Explain why 3 x 5 x 7 + 7 is a composite number.
Stuck on a question?
Paste any question from Exercise 1.3 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.
Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Not clearly stating the contradiction assumption at the start
- ✗Skipping steps in the proof — examiners want every line
- ✗Confusing 'rational' (p/q form) with 'irrational' (cannot be expressed as p/q)
Other Exercises in Chapter 1
Frequently Asked Questions
How many questions are in NCERT Class 10 Exercise 1.3?
Exercise 1.3 has 3 questions focused on proving irrationality of numbers like √2, √3, and √5 using proof by contradiction.
Is proving √2 is irrational important for boards?
Absolutely. This proof appears almost every year in CBSE board exams, usually as a 3-mark question. Learn it step by step.
Want to practise on paper? Download a free worksheet for this topic.
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