InterviewSolution
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InterviewSolution
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3. Prove that the following are irrationals(i) 75 |
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Answer» Let√2 be a rational number Therefore,√2= p/q [ p and q are in their least terms i.e., HCF of (p,q)=1 and q≠ 0 On squaring both sides, we get p²= 2q² ...(1)Clearly, 2 is a factor of 2q²⇒ 2 is a factor of p² [since, 2q²=p²]⇒ 2 is a factor of p Let p =2 m for all m ( where m is a positive integer) Squaring both sides, we get p²= 4 m² ...(2)From (1) and (2), we get 2q² = 4m² ⇒ q²= 2m²Clearly, 2 is a factor of 2m²⇒ 2 is a factor of q² [since, q² = 2m²]⇒ 2 is a factor of q Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1 Therefore, Our supposition is wrong Hence1/√2 is not a rational number i.e., irrational number. |
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