Prove that 5+3 root 2 is an irrational number

Answers (1)

To prove (5+3sqrt2) to be irrational.
First let's assume that it is a rational number,
(5+3sqrt2)=fracab,where a and b are integers.
Rightarrow 3sqrt2=fracab-5
Rightarrow 3sqrt2=fracab-frac5bb
Rightarrow sqrt2=fraca-5b3b  
Since RHS is rational	herefore sqrt2 will be rational too
But according to our own knowledge,sqrt2 is irrational.
There is contradiction,so,5+3sqrt2 is an irrational number.

Most Viewed Questions

Preparation Products

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
Knockout NEET (Nine Month Subscription)

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

₹ 13999/- ₹ 12499/-
Buy Now
Test Series JEE Main 2024

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 7999/- ₹ 4999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions