Question

Prove that
√7 is an irrational number.
​

Answer 1

Answer:

√7 is an irrational number.

Step-by-step explanation:

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.

Made me brainliest

Answer 2

root 7 is a irrational because,

number which are not rational are called irrational.

examples; root 6, root 27, 1.501001001..., root 7, and root 3 etc

and so many examples.

I hope it like you......

thank you so much

what is your name

my name is duhitha