Verified answer

Let P=2

3+5 is rational

on squaring both sides we get

P2=(23+ 5)2=(23)2 +( 5)2+2×23 × 5P2=12+5+415

P2=17+415

4P2−17 = 15 ………..(1)

Since P is rational no. therefore P

2 is also rational &

4P2 −17 is also rational.But

15is irrational & in equation(1)

4P2−17 = 15

Rational = irrational

Hence our assumption is incorrect & 2

3 + 5is irrational number.

b) P=(23 + 5 )(23 − 5)

P=12−5=7

Hence P is rational as qp= 17

& both p & q are coprime numbers.