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Let 16+17√3 be rational and let it's simplest form be p/q where p and q are integers and q≠0. Then, 16+17√3=p/q 17√3=p/q – 16 √3=p/q–16/17 …(i) Now, p/q is rational →(p/q–16/17) is rational [… difference of rational is rational] √3 is rational … from (i) The contradiction arises by assuming that √3 is rational. Hence, 16+17√3 is irrational.

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