Question

root2+5 rational or irrational?
answer fast i will brainlist you!

Answer 1

: Required Answer

$\longrightarrow$ Let us assume that √2+√5 is a rational number.

➝ A rational number can be written in the form of p/q where p,q are integers and q≠0

➝ √2+√5 = p/q

➝ On squaring both sides we get,

➝ (√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 incorrect

❍ √2+√5 is an irrational number.

Answer 2

✓2+5 is irrational number

Hope it's help you

Please mark me brainleast answer