Question

prove that 7-2√3 is irrational number​

Answer 1

Answer:

Let assume that 7-2root3 be rational and rational numbers are in the form of p/q form.

\begin{gathered}7 - 2 \sqrt{3} = \frac{p}{q} \\ 7 - \frac{p}{q} = 2 \sqrt{3} \\ \frac{7q - p}{q} = 2 \sqrt{3} \\ \frac{7q - p}{2q} = \sqrt{3} \end{gathered}

7−2

3

=

q

p

7−

q

p

=2

3

q

7q−p

=2

3

2q

7q−p

=

3

We know that root 3 is irrational and not p/q form. It contradicts the statement that it is irrational as it is p/q form.

Subtraction and multiplication of irrational number form irrational number so

7-2root3 is irrational.

Answer 2

Step-by-step explanation:

let us assume,to the contrary that 7-2√5is rational numbers.that is 7-2√3=a/b where a and b are two coprime(bis not equal to a)

7-2√3=a/b

but this contradicts the fact that7-2√5 is rational

this contradicts arise because of our incorrect assumption

so we concluded that 7-2√5is rational

hence prove