Prove that √2+3/√2 is an irrational number.
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let √2+3/√2 be rational.
so, √2+3√2=p/q (p,q are integers &q≠0)
=>(2+3)/√2=p/q
=>5/√2=p/q
=>√2=5q/p
since √2 is irrational but 5q/p is rational
=>√2≠5q/p
so, our assumption is wrong.
so,√2+3/√2 is an irrational number.(proved)
so, √2+3√2=p/q (p,q are integers &q≠0)
=>(2+3)/√2=p/q
=>5/√2=p/q
=>√2=5q/p
since √2 is irrational but 5q/p is rational
=>√2≠5q/p
so, our assumption is wrong.
so,√2+3/√2 is an irrational number.(proved)
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