Physics Gurukul1 Comment on Extra Questions For Class 10 Maths Chapter 1 Real Numbers Based On Irrationality of Numbers

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

Factorisation by Splitting the Middle Term With Questions
Extra Questions for Class 10 Maths Chapter 3 Linear Equations Based on Graphical Method of Solving Linear Equations
Extra Questions for Class 10 Maths Chapter 4 Quadratic Equations Based on Nature of Roots
Word Problems on Quadratic Equations for Class 10
Extra Questions For Class 10 Maths Chapter 2 Polynomials
Extra Questions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
Extra Questions For Class 10 Maths Chapter 5 Arithmetic Progression
Extra Questions For Class 10 Maths Chapter 1 Real Numbers Based On The Fundamental Theorem of Arithmetic
Extra Questions For Class 10 Maths Chapter 1 Real Numbers Based On Rational Numbers and Their Decimal Expansions
Extra Questions For Class 10 Maths Chapter 1 Real Numbers Based On Euclid’s Division Algorithm
Extra Questions For Class 10 Maths Chapter 1 Real Numbers Based On Euclid’s Division Lemma

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.

Click here for All Tests

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

  1. Ansh yadav February 13, 2023 — 8:07 pm

    Good question🙋🙋

    Reply

Leave a Reply

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

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