Question

show that
3√2-✓5 is an irrational ​

Answer 1

Solution==>

Let 3√2-5 be rational number,

•.• 3√2-5=a/b

where a and b are co-prime integers and

H.C.F of (a,b)=1

3√2-5=a/b

3√2=a/b+5

3√2=a+5b/b

√2=a+5b/3b

which is rational number

but, it contradicts the fact that √2 is irrational,

•.• our supposition is wrong that

H.C.F of (a,b)≠1

•.• 3√2-5 is irrational number.

Hence , showed or proved