prove that
is an irrational number.
Answers
Answered by
9
Assume √6 + √8 = a where a ∈ Q.
And √6 + √8 can be written in form of p/q where p, q are integers and q ≠ 0.
∴ a² = (√6 + √8)²
⇒ a² = 14 + 8√3
⇒ (a² - 14)/8 = √3
That means, √3 is a rational number. But this contradicts the fact that (√3) is an irrational number.
∴ (√6 + √8) is an irrational number.
More:-
Any real number which cannot be expressed in form of p/q where (p, q) ∈ Z and q ≠ 0 are called irrational numbers.
Expressions in form of √p where p is any prime number are irrationals.
Similar questions