Question

prove that 2+5√3 is an irrational number
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Answer 1

Answer:

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

Let, us assume that 2+5√3 is a rational number.Therefore, 2+5√3=a/b (where a and b are co prime)

5√3=a/b-2

5√3=a/b-25√3=a-2b/b

5√3=a/b-25√3=a-2b/b√3=a-2b/5b

Therefore, a-2b/5b is in the form of a/b which is rational number.But,this is contradicts the fact is that √3 is irrational number.Therefore, our assumption is wrong and 2+5√3 is an irrational number.

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Step-by-step explanation:

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Answer 2

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Let 2 + 5√3 be rational.

∴ 2 + 5√3 = p/q ; p, q are integers, q ≠ 0

⇒ √3 = (p/q - 2) ÷ 5

√3 = (p - 2q)/5q

LHS is irrational and RHS is rational which is a contradiction.

∴ 2 + 5√3 is irrational