Extra Questions For Class 10 Maths Chapter 1 Real Numbers Based On Irrationality of Numbers

Extra Questions On Irrationality of Numbers

Question: Prove that √5 is an irrational number.

Solution: Let √5 is a rational number then we have

√5=p/q, where p and q are co-primes.

⇒ p =√5q

Squaring both sides, we get

p2=5q2

⇒ p2 is divisible by 5

⇒ p is also divisible by 5

So, assume p = 5m where m is any integer.

Squaring both sides, we get p2 = 25m2

But p2 = 5q2

Therefore, 5q2 = 25m2

⇒ q2 = 5m2

⇒ q2 is divisible by 5

⇒ q is also divisible by 5

From above we conclude that p and q has one common factor i.e. 5 which contradicts that p and q are co-primes.

Therefore our assumption is wrong.

Hence, √5 is an irrational number.

Q.1. Prove that √2 is an irrational number.

Q.2. Prove that √3 is an irrational number.

Q.3. Prove that 2 + 5√3 is an irrational number.

Q.4. Prove that 3- 2√5 is an irrational number.

Q.5. Prove that √2 + √3 is an irrational number.

Q.6. Prove that √3 + √5 is an irrational number.

Related Posts

Category Lists (All Posts)

Select Category

All categories of this website are listed below with number of posts in each category for better navigation. Visitors can click on a particular category to see all posts related to that category.

Test Series (Engineering, Medical and School Level Exams)

Test series for students preparing for Engineering & Medical Entrance Exams are available. We also provide test series for School Level Exams. Tests for students studying in CBSE, ICSE or any state board are available here. Just click on the link and start test.

1 thought on “Extra Questions For Class 10 Maths Chapter 1 Real Numbers Based On Irrationality of Numbers

  1. Good question🙋🙋

Leave a Reply

✨Download Updated White Label Product Brochures (2023-24) 

%d bloggers like this:
search previous next tag category expand menu location phone mail time cart zoom edit close