Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove that the following are irrationals : 7 root 5

 Q3 (2)   Prove that the following are irrationals :

(ii) 7 \sqrt 5

Answers (1)

best_answer

Let us assume 7 \sqrt 5 is rational.

This means 7 \sqrt 5 can be written in the form \frac{p}{q} where p and q are co-prime integers.

\\7\sqrt{5}=\frac{p}{q}\\ \sqrt{5}=\frac{p}{7q}

As p and q are integers \frac{p}{7q}\\ would be rational, this contradicts the fact that \sqrt{5} is irrational. This contradiction arises because our initial assumption that 7 \sqrt 5 is rational was wrong. Therefore 7 \sqrt 5 is irrational.

Posted by

Sayak

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE 10th final date sheet 2026 out; exams till March 10, minor revisions after student protest
anam-khan

CBSE Board Exam 2026: Two exams for Class 10 ‘exhausting’ for teachers, cause more anxiety for students
anam-khan

Board Exams 2026: NCERT PARAKH forms expert committee to standardise Class 10, 12 certificates

Latest Question