1.

Prove that the following are irrationals (i) 7√5 (ii) 6+√2​

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Answer:

HOPE IT HELPS

Step-by-step explanation:

i)let us ASSUME THAT 7√5 is rational if possible

Then clearly

7√5= p/q [ q≠0 and p and q are co-prime ]

=> √5= p/7q

if p/q is rational then p/7q is also rational EVENTUALLY √5 is rational

But √5 is irrational

HENCE we arrive at contradictions

Therefore 7√5 is irrational

ii) Let us ASSUME THAT 6+√2 is rational if possible

Then Clearly

6+√2=p/q [ q≠0 and p and q are co-prime ]

=> √2= p/q - 6

Now if p/q is rational then p/q-6 is also rational, eventually √2 is rational

But √2 is irrational

Hence, we arrive at contradictions

Therefore, 6+√2 is irrational

                              [ proved (i) and (ii)]

Thank you

MARK AS BRAINLIEST !!!


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