Question

5+3√2prove it is irrational ​

Answer 1

let us assume to contrary that 5+ 3√2 is rational.

5+ 3√2= a/b   (let a and b be co- prime integers and b≠0)

3√2= a/b - 5

3√2= a-5b/b

√2= a- 5b/3b

⇒here a and b are integers and rational but it is equal to √2. and hence it is rational. and hence our assumption is wrong.

and hence, 5+ 3√2 is irrational.

Answer 2

Answer:Hi

Step-by-step explanation:

Now let us assume that 5+3√2 is rational

therefore , a/b=5+3√2                               (where a and b are co-primes)

therefore, gcd(a,b)=1

now,

5+3√2=a/b

3√2=5-a/b

√2= 5b-a/3b                                                   (by taking lcm)

but √2 is irrational

hence our assumption was wrong 5+3√2 is irrational

hence proved

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