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Prove that 3 + 2√5 is an irrational number

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asked Mar 14, 2018 in Mathematics by shabnam praween (19,050 points) ● 5 ● 6 ● 8
Prove that 3 + 2√5 is an irrational number

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answered Mar 14, 2018 by mdsamim (213,225 points) ● 5 ● 10 ● 15
selected Mar 20, 2018 by faiz
 
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Let us assume that 3 + 2√5 is rational

where p and q are integers, having no common factor except 1 and q ≠ 0.

√5 is also a rational number which is a contradition.

Hence, 3 + 2√5 is an irrational number.

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