Question

prove that root7 is irrational number. Hence prove that 3root7 - 5 is also an irrational number ​

Answer 1

Answer:

this is correct answer ( iam a teacher in world wide College)

Step-by-step explanation:

ANSWER

Let us assume that

7

is rational. Then, there exist co-prime positive integers a and b such that

7

=

b

a

⟹a=b

7

Squaring on both sides, we get

a

2

=7b

2

Therefore, a

2

is divisible by 7 and hence, a is also divisible by7

so, we can write a=7p, for some integer p.

Substituting for a, we get 49p

2

=7b

2

⟹b

2

=7p

2

.

This means, b

2

is also divisible by 7 and so, b is also divisible by 7.

Therefore, a and b have at least one common factor, i.e., 7.

But, this contradicts the fact that a and b are co-prime.

Thus, our supposition is wrong.

Hence,

7

is irrational.

Answer 2

Answer:

samas for chakradhari