Advertisement Remove all ads

Show that 5 + √ 7 is an Irrational Number. - Algebra

Advertisement Remove all ads
Advertisement Remove all ads
Short Note

Show that `5 +sqrt 7`  is an irrational number.

Advertisement Remove all ads

Solution

Let us assume that `5 +sqrt 7` is a rational number.

⇒ `5 +sqrt 7 = p/ q` , where p and q are two integers and q ≠ 0

⇒ `sqrt 7 = p/q - 5 = (p-5q)/q`

Since , p ,q and 5 are integers , so `(p - 5q)/ q` is a rational number.

⇒ `sqrt 7` is also a rational number.

But this contradicts the fact that `sqrt 7` is an irrational number.

This contradiction has arisen due to our assumption that  `5 +sqrt 7` is a rational number. 

Hence , `5 +sqrt 7` is an irrational number.

Concept: Concept of Rational Numbers
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 2 Real Numbers
Problem Set 2 | Q 4 | Page 35
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×