Question

Prove that 7+8 root 11 is irrational

Answer 1

Given

7+8√11

To prove

we have to prove 7+8√11 is a irrational number

$\sf\huge {\underline{\underline{{Solution}}}}$

Proof :

Let us assume that 7+8√11 is a rational number

so, it becomes

7+8√11 = a/b [ where a and b are co - prime numbers and b ≠ 0.

Solving 7+8√11 we get,

=> 8√11= a/b-7

=> 8√11= a-7b/b

=>√11= a-7b/8b

This shows that it's a rational number but √11 which is an irrational number so, our assumption that 7+8√11 is a rational number is wrong.

Thus , 7+8√11 is an irrational number

Hence, proved

Answer 2

Step-by-step explanation:

Refer to the attachment