Question

prove that 2+
root5 is irrationals
​

Answer 1

To prove:

√2+√5 is a irrational number

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 assumption is false.

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

_____________________

@zaqwertyuioplm

Answer 2

Step-by-step explanation:

here your answer

thanks