Question

prove,2√3+7 is an irrational number?​

Answer 1

Answer:-

→Let 2√3+7 be Rational

→i.e,2√3+7=$\frac{a}{b}$ [•°• Where a&b are Co-prime Integers, and a&b≠0]

→2√3=$\frac{a}{b}$-7

★Cross Multiply in RHS★

→2√3=$\frac{a-7b}{b}$

→√3=$\frac{a-7b}{2b}$

๛As √3 is Irrational and $\frac{a-7b}{2b}$ is Rational, Hence this creates Contradiction as Irrational≠Rational.Thus,2√3+7 is Irrational๛

$\rule{200}{2}$

Answer 2

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