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

Short Note

Show that 5 +sqrt 7  is an irrational number.

#### 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
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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 2 Real Numbers
Problem Set 2 | Q 4 | Page 35