Question

prove that 7 root 3 + root 5 is irrational​

Answer 1

Step-by-step explanation:

assume that 7√3+√5 is rational

so let x= 7√3+√5 for a rational no. x

=in x=7√3+√5,both side are rational as assumed

= now, x= 7√3+√5

=7√3=√5+x ( by exchanging)

= √3=√5+x /7

here, as both side of x = 7√3+√5 are rational,then RHS should be √3= (√5+x)/7.

But this contradicts our earlier assumption that 7√3+√5 is rational, because the RHS of √3=√5+x/7 is rational. While the LHS is irrational.

Hence proven