Show that each of the following numbers is a perfect square. In each case, find the number whose square is the given number:
(ii) 2601
(iii) 5929
(iv) 7056
(v) 8281
(i) 1225
In order to show that the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
1225 = 25 × 49
= 5 × 5 × 7 × 7
= (5 × 7) × (5 × 7)
= 35 × 35
= (35)2
Hence,
The given number is a perfect square.
And,
It is a perfect square of 35.
In order to show that the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
2601 = 9 × 289
= 3 × 3 × 17 × 17
= (3 × 17) × (3 × 17)
= 51 × 51
= (51)2
Hence,
The given number is a perfect square.
And,
It is a perfect square of 51.
In order to show that the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
5929 = 11 × 539
= 11 × 7 × 77
= 11 × 7 × 11 × 7
= (11 × 7) × (11 × 7)
= 77 × 77
= (77)2
Hence,
The given number is a perfect square.
And,
It is a perfect square of 77.
In order to show that the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
7056 = 12 × 588
= 12 × 7 × 84
= 12 × 7 × 12 × 7
= (12 × 7) × (12 × 7)
= 84 × 84
= (84)2
Hence,
The given number is a perfect square.
And,
It is a perfect square of 84.
In order to show that the given number is a perfect square,
At first,
We’ll resolve the given number into prime factors:
Hence,
8281 = 49 × 169
= 7 × 7 × 13 × 13
= (13 × 7) × (13 × 7)
= 91 × 91
= (91)2
Hence,
The given number is a perfect square.
And,
It is a perfect square of 91.