Question

prove that 7+3 root 5 is irrational number​

Answer 1

Answer:

Euclid's..

Step-by-step explanation:

⇒ Assume that 7 - 3√5 is rational.

    So let x = 7 - 3√5, for a rational number x.

⇒ In x = 7 - 3√5, both sides are rational as assumed.

⇒ Here, as both sides of x = 7 - 3√5 are rational,

   then so should be $\frac{7-x}{3} = \sqrt{5}$.  

    But this contradicts our earlier assumption that 7 - 3√5 is rational, because   the LHS of  $\frac{7-x}{3} = \sqrt{5}$   is rational while the RHS is irrational.

∴ 7 - 3√5 is irrational

⇒ Hence proved!!!