Let a natural number have the prime factorisation

MATHEMATICS · Single correct · CBSE · Mathematics · Real Numbers · Real Numbers

Problem

Let a natural number

k

have the prime factorisation

k=2^{a}\,3^{b}\,5^{c}\,7^{d}\dots

. Which condition on the exponents ensures that

\sqrt{k}

is a rational number? (a) At least one exponent is even. (b) All exponents are odd. (c) All exponents are even. (d) All exponents are multiples of

3