Question

p.t 2√3+√5 is irrational​

Answer 1

Step-by-step explanation:

Let us assume that 2

3

+

5

is rational number.

Let P=2

3

+

5

is rational

on squaring both sides we get

P

2

=(2

3

+

5

)

2

=(2

3

)

2

+(

5

)

2

+2×2

3

×

5

P

2

=12+5+4

15

P

2

=17+4

15

4

P

2

−17

=

15

………..(1)

Since P is rational no. therefore P

2

is also rational &

4

P

2

−17

is also rational.

But

15

is irrational & in equation(1)

4

P

2

−17

=

15

Rational



= irrational

Hence our assumption is incorrect & 2

3

+

5

is irrational number.

Answer 2

Answer:

This shows (a-3b)/2b is a rational number. But we know that √5 is an irrational number. So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect