Question

Write true (T) or false (F) for the following statements:
(i) $\sqrt{0.9}=0.3$
(ii) If $a$ is a natural number, then $\sqrt{a}$ is a rational number.
(iii) If $a$ is negative, then $a^2$ is also negative.
(iv) If $p$ and $q$ are perfect squares, then $\sqrt{\frac{p}{q}}$ is a rational number.
(v) The square root of a prime number may be obtained approximately, but never exactly.

Answer 1

(i) False, since the square of a number with one decimal will have two decimal places. Thus square of $0.3$ is $0.09$.
(ii) False, since square root of a natural number is not a rational number.
(iii) False, since the square of any negative number will be a positive number.
(iv) True. If $p$ and $q$ are perfect squares, then $\sqrt{\frac{p}{q}}$ is a rational number.
(v) True. The square root of a prime number may be obtained approximately, but never exactly.