using the prime factorisation method find which of the following number are perfect squares. a 441 b 576 c 11025 d 1176
Answers
Answer:
(i) 441
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
441 = 49 × 9
= 7 × 7 × 3 × 3
= (7 × 3) × (7 × 3)
= 21 × 21
= (21)2
Hence, it is a perfect square.
(ii) 576
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
576 = 64 × 9
= 8 × 8 × 3 × 3
= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
= (2 × 2 × 2 × 3) × (2 × 2 × 2 × 3)
= 24 × 24
= (24)2
Hence, it is a perfect square.
(iii) 11025
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
11025 = 441 × 25
= 49 × 9 × 5 × 5
= 7 × 7 × 3 × 3 × 3 × 3 × 5 × 5
= (7 × 5 × 3 × 3) × (7 × 5 × 3 × 3)
= 315 × 315
= (315)2
Hence,
It is a perfect square.
(iv) 1176
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
1176 = 7 × 168
= 7 × 8 × 21
= 7 × 2 × 2 × 2 × 7 × 3
Hence,
We can see that,
The number 1176 cannot be expressed as a product of two equal numbers.
Thus,
1176 is not a perfect square.