Question

3) Prove that √8 + 5 is irrational .
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Answer 1

Answer:

we can't further simplify so it is irrational

Answer 2

$\sqrt{8 } + 5 = \frac{a}{b} \\ \sqrt{8} = \frac{a}{b} - 5 \\ \sqrt{8} = \frac{a}{b} - \frac{5b}{b} (by \: taking \: lcm)$

where√8 is irrational

and a/b-5b/b is rational (a,b are integer)

so. the given is irrational

I hope it helps you