prove that 7+3 root 5 is irrational number
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5
♪Question:-
Prove that 7+3√5 is irrational
♦Proof:-
→Let 7+3√5 be rational
→i.e, 7+3√5= [where a&b are co-prime integers and a&b≠0]
★Shifting 7 to RHS★
→3√5=-7
★Cross multiply RHS★
→3√5=
★Shift 3 to RHS★
→√5=
•Since √5 is irrational and is rational, it creates a contradiction. Hence, 7+3√5 is irrational.
Answered by
2
Let , 7 + 3√5 is an rational number
Here , √5 is an irrational number but (a - 7b)/3b is an rational number
Since , Irrational number ≠ rational number
Thus , our assumptions is wrong
Hence , 7 + 3√5 is an irrational number
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