Q. 15.0( 2 Votes )

If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number.

Answer :

Rational Number is a number that can be expressed in the form p/q, where q not equal to zero.

Let there be two rational numbers x and y

There product will be equal to xy, and also will be in p/q form

Product of two rational number is always a rational number.

Hence if a is a rational number, then

a2 = a x a is a rational number,

a3 = a2 x a is a rational number.

... an = a x a x a x a...... to n times is a rational number.

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