Question

if root 3 is irrational number then prove that 3 + 7 root 3 is also an irrational number​

Answer 1

Answer:

let us assume that 3 +7√3 is a rational number.

now let 3 +7√3 =a/b (a and b are co primes and b≠zero)

so 7√3 = a/b - 3

or

√3= a/7b - 3/7

since a and b are integers,therefore

a/7b - 3/7 is a rational number

hence, √3 is a rational number.

but √3 is an irrational number.

this shows that our assumption is in correct

so,3 +7√3 is an irrational number.

Answer 2

You'll find your ans in the attachment.

Hope it helps.

Thankyou!