Sarthaks Test
0 votes
in Mathematics by (15.5k points)
Prove that √3 + √5 is an irrational number

1 Answer

0 votes
by (22.3k points)
selected by
Best answer

If possible, let 3 + 5 be a rational number equal to x. Then,

Now, x is rational 

=> x2 is rational 

=> x2 - 8/2 is rational

=> 15 is rational

 But, 15 is rational 

Thus, we arrive at a contradiction. So, our supposition that 3 +5  is rational is wrong. 

Hence, 3 + 5  is an irrational number.

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.