Question

prove that 4-5root2 is irrational ​

Answer 1

Answer:

so, (4-5√2) = p/q. so, 4-5√2 is an irrational number... Since a, b are integers, then (a − 4b)/(−5b) represents a rational number.

Answer 2

• Let x = 4 - 5√2 be rational number .

→ x = 4 - 5√2

Now,

Squaring on both side , we get

( x )² = ( 4 - 5√2 )²

→ x² = 4² + (5√2)² - 2(4) (5√2)

→ x² = 16 + 50 - 40√2

→ x² = 66 - 40√2

→ x² - 66 = -40√2

→ 66 - x² / 40 = √2

• 66 - x²/40 is a rational number .
• /40 is a rational number .√2 is a irrational number.

Hence,

• 4 - 5√2 is a irrational number

† proved †