Question

Prove That 2 Root 5 Is Irrational​

Answer 1

Answer:

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

Answer:

assume that 2 root 5 is rational where p and q are co prime and q not equal to 0

2 root 5 = p/q

root 5 = p/2q

here root 5 is an irrational number and p /2q is rational number

this a condradiction to our assumption that 2 root 5 is a rational number.

therefore our assumption is wrong. that is 2root5 is an irrationalnumber .

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