Question

Show that 5+√7 is an irrational number.

Answer 1

Answer:

Let 5+2√7 be a rational no.

therefore 5+2√7=p/q

2√7=p/q-5

2√7=p-5q/q

√7=p-5q/2q

therfore p-5q/2q ia a rational no.

therefore √7 is also a rational number

but it is not possible as root 7 is an irrational no. therefore our assumption is wrong

Therefore 5+2√7 is an irrational number..

Answer 2

To prove : 5+√7 is an irrational number.

Proof :

Let us assume 5+√7 as rational number.

Rational number is in the form of $\frac {p}{q}$

$= 5+√7 = \frac {a}{b}$

= √7 = a/b- 5

= a-5b/√7b

= a-7b/√5b

• Our assumption or contradiction that 5+√7 is a rational number is false.
• 5+√7 is an irrational number.

•°• Hence proved.