Question

Prove that √3+2√5 is an irrational number

Answer 1

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Let us assume that 5  3 2  is a rational number.

7. Given 2 is irrational, prove that Solution.

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53 2 p whereq0 andpandqareintegers. q

2  p  5q 3q

2 is a is a rational number as RHS is rational . This contradicts the given fact that 2 is irrational.