Question

Show that each of the following numbers is a perfect square. Also, find the the square root of each.
1. 1225
2.3969
3. 2601
4. 5929
5. 7056​

Answer 1

Answer:

(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.

(iii) 2601

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.

(iv) 5929

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.

(v) 7056

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.