Is root 3 rational or irrational

Answers (1)

√3 is a irational number. Lets proof

Lets say that √3 is artional number, so it can be represented as p/q, where p and q have no common factors.

So √3 = p/q

  3 = p2/q2

3 q2=p2

Now p2 must be divisible by 3 and then p must be divisible by 3.

p=3k

3q2= (3k)2

3q2= 9k2

q2= 3k2

now we have a contradiction. so √3 is a irational number

Most Viewed Questions

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions