1.

Given that under root 3 is irrational,prove that 5+2under root 3 is irrational number.

Answer»

5 + 2√3 is irrational number

__________ [TO PROVE]

Let us ASSUME that, 5 + 2√3 is a rational number

=> 5 + 2√3 = \dfrac{a}{<klux>B</klux>}

Here, a and b are co-prime numbers.

=> 2√3 = \dfrac{a}{b} - 5

=> 2√3 = \dfrac{a\:-\:5b}{b}

=> √3 = \dfrac{a\:-\:5b}{2b}

Here..

\dfrac{a\:-\:5b}{2b} is rational number.

So, √3 is also a rational number.

But √3 is irrational number ____ [GIVEN]

So, our ASSUMPTION is wrong.

5 + 2√3 is irrational number.

___________ [HENCE PROVED]


Discussion

No Comment Found

Related InterviewSolutions