Grade 1210 grade maths
Prove that the following are irrationals: 6 + √2????????????????????
Prove that the following are irrationals:
6 + √2????????????????????
1 Answer
Harshit Singh
Dear Student
Let us assume6 +√2is a rational number.
Then we can find co-primes x and y (y ≠ 0) such that6 +√2= x/y⋅
Rearranging, we get,
√2= (x/y) - 6
Since, x and y are integers, thus (x/y) - 6 is a rational number and therefore,√2is rational. This contradicts
the fact that√2is an irrational number.
Hence, we can conclude that6 +√2is irrational.
Thanks
Let us assume6 +√2is a rational number.
Then we can find co-primes x and y (y ≠ 0) such that6 +√2= x/y⋅
Rearranging, we get,
√2= (x/y) - 6
Since, x and y are integers, thus (x/y) - 6 is a rational number and therefore,√2is rational. This contradicts
the fact that√2is an irrational number.
Hence, we can conclude that6 +√2is irrational.
Thanks
Other Related Questions on 10 grade maths
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)
10 grade maths
Last Activity: 11 Months ago
The smallest composite number is ______.
(a) 2
(b) 4
(c) 1
(d) None of these
The smallest composite number is ______.
(a) 2
(b) 4
(c) 1
(d) None of these
10 grade maths
Last Activity: 0 Years ago
Find the arithmetic mean of the first ten odd natural numbers.
Find the arithmetic mean of the first ten odd natural numbers.
10 grade maths
Last Activity: 0 Years ago