Question

Prove that 7 + 2√3 is an irrational number.


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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.

Step-by-step explanation:

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