Prove that is (√3 + √7) irrational.

Question

KnowledgeBoat · Accepted Answer

Let us assume is a rational number. Let, Squaring both sides, we get : Here, x is rational, ∴ x2 is rational .........(1) ⇒ x2 - 10 is rational (As difference between two rational numbers is always rational) ⇒ is rational (Dividing two rational numbers results in a rational number) But, is irrational. is irrational. Thus, x2 - 10 is irrational and so x2 is irrational ........(2) (1) and (2) do not match with each other. ∴ We arrive at a contradiction. So, our assumption that is a rational number is wrong. ∴ is irrational. Hence, proved that is an irrational number.

Mathematics

Prove that is (√3 + √7) irrational.

Rational Irrational Nos

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