Question

prove that 1/√12 is irrational ?

Answer 1

Let us assume that 1/√ 12 is rational number.

1/√12 =p/q [where p and q are rational and q is not equal to zero. ]

Multiply both numerator and denominator by √ 12.

1/√12×√12/√ 12 = p/q.

√12/12=p/q.

√12 =12p/q.

LHS is not equal to RHS.

Irrational is not equal to rational.

Since, √ 12 is irrational.

Thus we can say that 1/√12 is also irrational.

Hope it helps.