Question

prove that √2+√7 is an irrational
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

supose √2+√7 is not an irrational number

=√2+√7 is a rational number

= √2+√7 =p/q ------------ 1

=√2= p/q - √7 ---------- 2

( squaring on both sides)

= (√2)^2= (p/q - √7)^2

= 2 = p^2/q^2 + 7 - 2√7p/q

{ (a-b)^2=a^2+b^2-2ab }

= 2*√7p/q = p^2/q^2 + 5

=√7 = p^2 + 5q^2

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2pq

√7 is irrational and p^2 + 5q^2 is rational

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2pq

hence, there is a contradiction

because an irrational number cannot be equal to the rational number.

√2+√7 is an irrational number.

I HOPE IT IS HELPFUL TO YOU.