Q. 24.2( 10 Votes )

# Show that each of

Answer :

(i) 1156

Resolving 1156 into prime factors we get,

1156 = 2 × 2 × 17 × 17

Now, grouping the factors into pairs of equal factors

We get,

1156 = (2 × 2) × (17 × 17)

As all factors are paired

Hence, 1156 is a perfect square

Again,

1156 = (2 × 17) × (2 × 17)

= 34 × 34

= (34)2

Thus, 1156 is a square of 34

(ii) 2025

Resolving 2025 into prime factors we get,

2025 = 3 × 3 × 3 × 3 × 5 × 5

Now, grouping the factors into pairs of equal factors

We get,

2025 = (3 × 3) × (3 × 3) × (5 × 5)

As all factors are paired

Hence, 2025 is a perfect square

Again,

2025 = (3 × 3 × 5) × (3 × 3 × 5)

= 45 × 45

= (45)2

Thus, 2025 is a square of 45

(iii)14641

Resolving 14641 into prime factors we get,

14641 = 11 × 11 × 11 × 11

Now, grouping the factors into pairs of equal factors

We get,

14641 = (11 × 11) × (11 × 11)

As all factors are paired

Hence, 14641 is a perfect square

Again,

14641 = (11 × 11) × (11 × 11)

= 121 × 121

= (121)2

Thus, 14641 is a square of 121

(iv) 4761

Resolving 4761 into prime factors we get,

4761 = 3 × 3 × 23 × 23

Now, grouping the factors into pairs of equal factors

We get,

4761 = (3 × 3) × (23 × 23)

As all factors are paired

Hence, 4761 is a perfect square

Again,

4761 = (3 × 23) × (3 × 23)

= 69 × 69

= (69)2

Thus, 4761 is a square of 69

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