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Maths / Real Numbers / Irrational Numbers
QUESTION
 

Show that 7-sqrt3 is irrational.

EXPLANATION
Explain TypeExplanation Content
Text

let 7-sqrt3 be a rational number. therefore 7-sqrt3=frac{a}{b} ,where'a' and 'b' are co-prime integers,bneq 0          (1)   therefore from (1) 7-frac{a}{b}=sqrt3   Rearranging this equation,we get

sqrt3=7-frac{a}{b}=frac{7b-a}{b}  Since 'a' and 'b' are integers,we get 7-frac{a}{b} as rational. so,sqrt3 : is : rational.  But this contradicts the fact because sqrt3 is irrational. So,we conclude that 7-sqrt3 is irrational.

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