Question

Prove that 5+2√3 is an irrational no. if √3 is an irrational number.

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Answer 1

Step-by-step explanation:

given that √3 is an irrational no.

let 5+2√3 be a rational no.

so 5+2√3 = p/q

5q+2√3q= p

√3 = p-5q/2q

on lhs = √3

= irrational no.

and on RHS = p-5/ 2q

= rational no.

so lhs is not equal to RHS

therefore it is contradiction

our assumption has been proved wrong

so, given no. 5+2√3 is an irrational no.

Answer 2

Answer:

let's accume that 5+2√3 us rational number and have co-prime factor a and b

5+2✓3=a/b

2√3=a/b-5

2√3=a-5b/b

√3=a-5b/2b

(we have given that√3 is irrational number but, irrational cannot be equal to rational number)

√3 is not equal to a-5b/2b