prove that 3 + 2 \sqrt{7 =} us an irrational ​

Question

prove that
3 + 2 \sqrt{7 =}
us an irrational

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Margaret 2 months 2021-12-03T05:41:09+00:00 2 Answers 0 views 0

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    0
    2021-12-03T05:42:22+00:00

    Answer:

    16807

    Hope it helps……..

    0
    2021-12-03T05:42:46+00:00

    \rm\huge\blue{\underline{\underline{ Question : }}}

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

    \rm\huge\blue{\underline{\underline{ Solution : }}}

    Let us assume that 3 + 2√7 is a rational number.

    \sf\:\implies 3 + 2\sqrt{7} = \frac{a}{b}

    • [ a & b are co – primes. ]

    \sf\:\implies 2\sqrt{7} = \frac{a}{b} - 3

    \sf\:\implies 2\sqrt{7} = \frac{a - 3b}{b}

    \sf\:\implies \sqrt{7} = \frac{a - 3b}{2b}

    ↪ Now, (a – 3b)/2b is a rational number. And √7 is an irrational number.

    ↪ So our assumption is wrong.

    ↪ This assumption has arisen because we assumed that 3 + 2√7 is a rational number.

    \underline{\boxed{\bf{\purple{ \therefore 3 + 2\sqrt{7}\: is \:an\: irrational \:number.}}}}\:\orange{\bigstar}

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