prove 3+2√5 is irrational it is given that √5is irrational​

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prove 3+2√5 is irrational it is given that √5is irrational​

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1 month 2021-08-14T07:58:45+00:00 2 Answers 0 views 0

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    0
    2021-08-14T08:00:36+00:00

    \huge\boxed{\underline{\underline{\green{\tt Solution}}}}

    If possible let

    3 + 2 \sqrt{5} \: \:  \:  is \: rational

     \implies \: 3  + 2 \sqrt{5}  - 3 \:  \: is \:  \: rational

     \implies \: 2 \sqrt{5}  \:  \:  \: is \:  \: rational

     \implies \:  \frac{2 \sqrt{5} }{2}  \:  \: is \:  \: rational

     \implies \:  \sqrt{5}  \:  \:  \: is \:  \: rational

    But this contradicts the given fact that

     \sqrt{5} \: \:  \:  is \: irrational

    Hence

    3 + 2 \sqrt{5} \: \:  \:  \:  is  \:  \: \: irrational

    \displaystyle\textcolor{red}{Please \:  Mark \:  it  \: Brainliest}

    0
    2021-08-14T08:00:37+00:00

    To prove: 3 + 2√5 is an irrational number. Proof: Let us assume that 3 + 2√5 is a rational number. This shows (a-3b)/2b is a rational number

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