Using the prime factorization method, find which of the following numbers perfect squares are:
(i) 441 (ii) 576
(iii) 11025 (iv) 1176
(v) 5625 (vi) 9075
(vii) 4225 (viii) 1089
(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.
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.
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)
= 24 × 24
= (24)2
Hence,
It is a perfect square.
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.
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
5625 = 225 × 25
= 9 × 25 × 25
= 5 × 5 × 5 × 5 × 3 × 3
= (5 × 5 × 3) × (5 × 5 × 3)
= 75 × 75
= (75)2
Hence,
It is a perfect square.
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
9075 = 25 × 363
= 25 × 3 × 121
= 5 × 5 × 3 × 11 × 11
= 25 × 3 × 121
Hence,
We can see that,
The number 9075 cannot be expressed as a product of two equal numbers.
Thus,
9075 is not a perfect square.
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
4225 = 25 × 169
= 5 × 5 × 13 × 13
= (5 × 13) × (5 × 13)
= 65 × 65
= (65)2
Hence,
It is a perfect square.
In order to find if the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
1089 = 121 × 9
= 11 × 11 × 3 × 3
= 11 × 11 × 3 × 3
= (11 × 3) × (11 × 3)
= 33 × 33
= (33)2
Hence,
It is a perfect square.