A Square and a Cube

Aisha says 1962 could be the square of some whole number, if the right number is found, since it is a large number. Kunal says just looking at the last digit alone can prove it is not a perfect square. Who is right?

Riya says the square root of 64 is 32, because a square root means halving — undoing a doubling. Aman says the square root of 64 is 8. Who is right?

Kabir knows the sum of the first n odd numbers always equals n² (like 1+3+5=9=3²). He says the same rule will apply to even numbers too — the sum of the first n even numbers will also be n². Is Kabir right?

Priya says any number's cube is always bigger than its square, since cubing involves one extra multiplication. Is that true for every whole number?

A square tile is 10 cm on each side. Ravi says if you double the side to 20 cm, the area doubles too. Sara says the area becomes four times as big. Who is right?

Rohan says 12 (= 2 × 2 × 3) must be a perfect square, since it breaks down cleanly into prime numbers. His teacher says breaking into prime factors alone is not enough. Who is right?