Question

prove that 2√5 in irrational​

Answer 1

Step-by-step explanation:

If possible, let us assume 2+

5

is a rational number.

2+

5

=

q

p

where p,q∈z,q



=0

2−

q

p

=−

5

q

2q−p

=−

5

⇒−

5

is a rational number

∵

q

2q−p

is a rational number

But −

5

is not a rational number.

∴ Our supposition 2+

5

is a rational number is wrong.

⇒2+

5

is an irrational number.

Answer 2

Step-by-step explanation:

We conclude that √5 is an irrational number. We can write 2 as 21, thus observing that it is a rational number. We know that a sum of a rational number and an irrational number is an irrational number. Hence, we observe that 2+√5 is an irrational number.