Question

Prove that under root 6+ under root 5 is irrational.

Answer 1

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers.

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-(√5+√6)²= (p/q)²

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-(√5+√6)²= (p/q)²5+6+2√30= p²/q²

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-(√5+√6)²= (p/q)²5+6+2√30= p²/q²p²/2q² +5 +6 =√30

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-(√5+√6)²= (p/q)²5+6+2√30= p²/q²p²/2q² +5 +6 =√30As we know that √30 is irrational.

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-(√5+√6)²= (p/q)²5+6+2√30= p²/q²p²/2q² +5 +6 =√30As we know that √30 is irrational.Here LHS is irrational and RHS is in the form of p/q so it is rational.

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-(√5+√6)²= (p/q)²5+6+2√30= p²/q²p²/2q² +5 +6 =√30As we know that √30 is irrational.Here LHS is irrational and RHS is in the form of p/q so it is rational.Any rational no. cannot be equal to irrational no.

Let √6+√5 be rational no. so it can be written in the form of p/q where q is not equal to zero and p and q are co prime integers. So, √5+√6=p/q Squaring both the sides-(√5+√6)²= (p/q)²5+6+2√30= p²/q²p²/2q² +5 +6 =√30As we know that √30 is irrational.Here LHS is irrational and RHS is in the form of p/q so it is rational.Any rational no. cannot be equal to irrational no.Hence, √5+√6 is irrational.