If √ab is an irrational number,prove that √a+√b is rational
Answers
Answered by
3
Answer:
let ✓a +✓b be a rational no.
equals to p/q where qis not equal to zero
✓a + ✓b = p/q
squaring on both the side
(✓a+✓b)² = (p/q)²
using the identity (a+b)² = a²+b²+2ab
(✓a)² +(✓b)²+2✓a✓b = (p/q)²
a+b+2✓ab =(p/q)² [hence ✓a✓b = ✓ab]
shifting ...
2✓ab = (p/q)² - (a+b)
✓ab = { (p/q)² - (a+b) } /2
hence rational no. is not equal to irrational no.
as because ✓ab is an irrational no. which is given
hense it's a irrational no..
then ✓a +✓b is not a rational no
Similar questions
Physics,
6 months ago
Geography,
6 months ago
Math,
6 months ago
Physics,
1 year ago
Business Studies,
1 year ago