Question

Which of the numbers below are squares of fractions?

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Answer 1

For a number to be a square of a fraction, both the numerator and denominator of the fraction should be square numbers.

(i) The denominator of is 15, which is not the square of any number.

So, is not the square of any fraction.

(ii) The numerator of is 8, which is not the square of any number.

So, is not the square of any fraction.

(iii) The numerator and denominator of are 16 and 25, respectively, which are the squares of the numbers 4 and 5.

So, is the square of the fraction.

(iv)

The numerator and denominator of are 9 and 4, respectively, which are the squares of the numbers 3 and 2.

So, is the square of the fraction.

(v)

The numerator of is 37, which is not the square of any number.

So, is not the square of any fraction.

(vi) The numerator and denominator of are 8 and 18, respectively, which are not the squares of any numbers.

So, is not the square of any fraction.