Question

prove that 5+✓2 is a irrational no

Answer 1

hey mate here is your answer

so here;
we have to prove 5+√2 is irrational no.
let us take the opposite
5+√2 is rational no.

hence 5+√2 can be written in the form a/b
where a and b are co-prime

hence;
5+√2=a/b
√2=a/b-5
√2=a-5b/b
therefore,LHS is irrational & RHS is rational no.

LHS is not equal to RHS

thia contradicts that 5+√2 is irrational no

hence 5+√2 is irrational

HENCE THE PROOF

hope this helps u mate if it does pls mark as brainliest

be blessed

good night dear mate❤❤

Answer 2

Answer:

Step-by-step explanation:

Let √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.