Question

prove 4+√3 is irrational​

Answer 1

Question:

Prove that 4+√3 is irrational number.

Note:

• Irrational no. : The number which cannot be written in the form of p/q where p and q are integers but q≠0 are called irrational number.

Eg: √2 , √3 , π , 1.1175224472157..... etc

Proof:

Let us assume that the given number is rational thus it may be written in form of p/q .

Thus,

=> 4+√3 = p/q

=> √3 = p/q - 4

=> √3 = (p-4q)/q --------(1)

Also,

=> If p/q is rational then p/q - 4 is also rational.

=> If p/q - 4 is rational then (p-4q)/q rational.

=> If (p-4q)/q is rational then √3 is also rational.

{ using eq-(1) }

Clearly,

From eq-(1) , we get that , √3 is rational which contradics the fact that√3 is an irrational number.

Thus,

Our assumption is wrong and hence 4 + √3 is irrational number.

Hence proved.