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Q. 24.2( 6 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 :

a is a positive rational number (Given)

The product of two rational numbers is always a rational number. Hence if a is a rational number then-

a ² = a × a is also a rational number,
a ³ = a ² × a is also a rational number,
a ⁴ = a ³ × a is also a rational number,

…
∴ a ⁿ = a ^n-1 × a is a rational number.

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PREVIOUS Write the following rational numbers in decimal form: (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) NEXTFind three rational numbers lying between 0 and 0.1. Find twenty rational numbers between 0 an 0.1. Give a method to determine any number of rational numbers between 0 and 0.1.

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