Question

1. Which of the following natural numbers are perfect squares? Give reasons in support of your answer.
(i) 729
(ii) 5488
(iii) 1024
(iv) 243​

Answer 1

Answer:

729 is the righ answer

pls support me

Answer 2

Answer:

1. 729 = 3 × 3 × 3 × 3 × 3 × 3

729 is the product of pairs of equal prime factors

Therefore, 729 is a perfect square.

2. 5488 = 2 × 2 × 2 × 2 × 7 × 7 × 7

After pairing the same prime factors, one factor 7 is left unpaired.

Therefore, 5488 is not a perfect square.

3. 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

After pairing the same prime factors, there is no factor left.

Therefore, 1024 is a perfect square

4. 243 = 3 × 3 × 3 × 3 × 3

After pairing the same prime factors, factor 3 is left unpaired.

Therefore, 243 is not a perfect square.