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5-√3is a irrational number

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5-√3is a irrational number

Posted by Rocky ☯️ 1 year, 9 months ago

CBSE > Class 10 > Mathematics

2 answers

Taniya . 1 year, 9 months ago

Let us assume, 5−√3 is a rational number ⇒5−√3=qp, where p,q∈z,q=0 5−qp=√3 ⇒q5q−p=√3 ⇒√3 is a rational number ∵q5q−p is rational but √3 is not a rational number. This gives us a contradiction. ∴ our assumption that 5−√3 is a rational number is wrong ⇒5−√3 is an irrational number.

Aditya Verma 1 year, 9 months ago

Let we assume that 5-√3 is rational.so we can write is on p/q where pq are coprime and q not equal to 0 5-√3=p/q √3=p/q-5 So p/q is integers so therefore √3 is rational But we know the fact that √3 is irrational Our assumption get wrong so therefore 5-√3 is irrational Hence proved....

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