Question

prove that 11/√7 is irrational
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Answer 1

Answer:

∴ 11+√7 is an irrational number

Step-by-step explanation:

let us assume to the contrary that 11+√7 is rational such that:

=> 11+√7 = $\frac{p}{q}$

=>√7 = $\frac{p}{q}$ - 11

=>√7 =   $\frac{p - 11}{q}$

Since, √7 is irrational but we have prove that √7 is equal to a rational number, i.e in the form $\frac{p}{q}$.

This contradiction arose due to our wrong assumption.

∴ 11+√7 is an irrational number