Question

prove that 5-3√3/7 is irrational no​

Answer 1

considering 5- 3√3/7 is a rational number.

so,

5-3√3/7 = p/q

-3√3/7 = p/q - 5

√3 = (p - 5q/q)( 7/-3)

√3≠ 7p - 35q/ -3

hence, LHS≠RHS as lhs is an irrational and rhs is rational number so our assumption got wrong and its an Irrational number.

proved!

Answer 2

Answer:

yes it is irrational

Step-by-step explanation:

Let 5-3√3/7 be rational, then-----------------------------(statement 1)

5-3√3/7=p/q__________________(as any rational no. can be expressed in the form of p/q, where p and q are integers and q is not equal to 0)

5-3√3=p/q-5

3√3=(7p-35q)/q

√3=(7p-35q)/3q

now the equation at the right side is rational as p and q are integers but √3 is not rational

according to statement 1 the equation is contradicting(i.e.LHS is irrational and RHS is rational.

Hence, 5-3√3/7 is irrational.