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Maths / Real Numbers / Irrational Numbers
QUESTION
 

Show that large 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, b neq0   (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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