Question

Show that 3+√7is irarational no give that √7 irrational

Answer 1

Answer:

given: √7 is irrational number.

to prove: 3+√7 is irrational number.

proof:

let 3+√7 be a rational number.

ie. it can be written in the form of p/q.

thus,

=> 3+√7=p/q

=> √7=p/q - 3

=> √7=(p-3q)/q

since, p/q is rational,

thus,p/q - 3 is rational,

thus, (p-3q)/q is rational.

it contradict the fact that , √7 is an irrational number.

thus , the conclusion is that, 3+√7

is an irrational number.

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