prove that root 5 is an irrational number and then show that 2 root 5 + 3 is also irrational
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Say, √5 is a rational number. ∴ It can be expressed in the form p/q where p,q are co-prime integers. ... For you second query, as we've proved √5 irrational. Therefore √5+3 is also irrational because sum of a rational and an irrational number is always an irrational number.
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