Question

prove that 2√3 + √5 is an irrational number​

Answer 1

Let 2√3 + √5 be rational numbers

2√3 + √5 = a/b { a,b are integers b is not equal to zero}

2√3 + √5 = a/b

2√3 = a/b - √5

2√3 = a - √5b/b { After LCM }

√3 = a - √5b/2b

3= (a -√5b/2b)^2

3 = a^2 - 2√5ab +5b/4b^2

Rational = Irrational

.°. Our assumption is wrong

.°. 2√3 + √5 is Irrational.

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