Question

prove that root 2- root 5 is a irrational no

Answer 1

et √2+√5 be a rational number.
A rational number can be written in the form of p/q where p,q are integers.
√2+√5 = p/q
Squaring on both sides,
(√2+√5)² = (p/q)²
√2²+√5²+2(√5)(√2) = p²/q²
2+5+2√10 = p²/q²
7+2√10 = p²/q²
2√10 = p²/q² - 7
√10 = (p²-7q²)/2q
p,q are integers then (p²-7q²)/2q is a rational number.
Then √10 is also a rational number.
But this contradicts the fact that √10 is an irrational number.
.°. Our supposition is false.
√2+√5 is an irrational number.
Hence proved.

Answer 2

to proof(√2-√5) is an irrational number
√2 is an irrational number and
√5 is also an irrational number
and difference of two irrational numbers is irrational number
so,(√2-√5) is an irrational number