Math, asked by roshandash88gmailcom, 1 year ago

show that √5-√7 is an irrational number​

Answers

Answered by mysticd
1

Solution:

Let us assume (√5-√7) is a

rational number.

√5-√7 = a/b

Where a,b are integers and

b≠0

On Squaring both sides, we get

=> (√5-√7)² = (a/b)²

=> (√5)²+(√7)²-2*√5*√7=a²/b²

=> 5+7-2√35 = a²/b²

=> 12 - 2√35 = a²/b²

=> 12+a²/b² =2√35

=> (12b²+a²)/b² = 2√35

=> (12b²+a²)/2b² = √35

Since , a,b are rational number, (12b²+a²)/2b² is

rational. So, √35 is rational.

But , it contradicts that the fact that √35 is an irrational.

Therefore,

(√5-√7) is an irrational.

••••

Similar questions