Question

PROVE THAT THE√2-3√5 IS A IRRATIONAL NUMBER​

Answer 1

Answer:

Let us assume that 2√3+√5 is rational number.

Let P = 2√3+√5 is rational

on squaring both sides we get

p2 = (2√3+√5)² = (2√3)² + (√5)²+2 x 2√3 x √5

P² = 12 +5+4√15

p² = 17+ 4√15

P² - 17

15(1)

Since P is rational no. therefore P² is also rational & P²-17 is also rational. 4

But √15 is irrational & in equation (1)

P² - 17 4 √15

Rational is not equal to irrational

Hence our assumption is incorrect & 2√3+√5 is irrational number.

P = (2√3+√5) (2√/3 – √5)

P=125=7

72

Hence P is rational as P/q = 7/1 q are coprime numbers. = & both p &