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Prove that root 17 is a …

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Prove that root 17 is a irrational number

Posted by Piyush Rajpurohit 1 year, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Shivam Kumar 1 year, 6 months ago

Let, assume that ✓17 is rational number. We will prove it by contradiction ✓=p/q, ( where p and q are coprime integer & q does not = 0) Squaring on both sides (✓17)2 = (p/q)2 17= p2/q2 P2 = 17 q2 < first equation Here 17 divide p and 17 divide p2 also P2/17= c , ( where c is any positive integer) P2 = 17c Squaring on both sides P2 = 289c2 < second equ From 1 and 2 17c = 289 c2 c = 17 c2 17 divide c and 17 divide c2 also We can observe that 17 is common factor of p and q This contradict the fact that p and q are coprime So, our assumption that✓17 is rational is wrong Hence, proved that ✓17 is irrational

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