Question

2. For each of the following find the smallest sumber by which it should be multiplied so as to get
a perfect square. Also find the square root of the perfect square
(I) 1250
(ii) 7350
(III) 47068
(iv) 1300
(v) 24000​

Answer 1

Solutions of the questions

i)  1250

To find the smallest number by which it should be multiplied so as to get

a perfect square , let us do the prime factorization of 1250.

1250 =  2 × 5 × 5 × 5 × 5

✩ Here , 2 is the unpaired number so 1250 must be multiplied with 2 to get a perfect square.

⇒1250 × 2 = 2500

⇒ √2500 = 50

✳ Square root = 50.

(ii) 7350

To find the smallest number by which it should be multiplied so as to get

a perfect square , let us do the prime factorization of 7350.

7350 =  2 × 3 × 5 × 5 × 7 × 7

✩ Here , 2 and 3 are the unpaired numbers so 7350 must be multiplied with 2×3 = 6 to get a perfect square.

⇒ 7350 × 6 = 44100

⇒ √44100 = 210

✳ Square Root = 210.

(iii) 47068

To find the smallest number by which it should be multiplied so as to get

a perfect square , let us do the prime factorization of 47068.

47068 = 2 × 2 × 7 × 41 × 41

✩ Here , 7 is the unpaired number so 47068 must be multiplied with 7 to get a perfect square.

⇒ 47068 × 7 = 329476

⇒ √329476 = 574

✳ Square Root = 574.

(iv) 1300

To find the smallest number by which it should be multiplied so as to get

a perfect square , let us do the prime factorization of 1300.

1300 = 2 × 2 × 5 × 5 × 13

✩ Here , 13 is the unpaired number so 1300 must be multiplied with 13 to get a perfect square.

⇒ 1300 × 13 = 16900

⇒ √16900 = 130

✳ Square root = 130.

(v) 24000​

To find the smallest number by which it should be multiplied so as to get

a perfect square , let us do the prime factorization of 24000.

24000 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5 × 5

✩Here , 3 and 5 are the unpaired numbers so 2400 must be multiplied with 5 × 3 = 15 to get a perfect square.

⇒ 24000 × 15 = 360000

⇒ √360000 = 600

✳ Square root = 600.

Answer 2

Answer:

i) 1250

1250=2×5×5×5×5

1250×2 = 2500

√2500 =50

ii) 7350

7350= 2×3×5×5×7

2×3 =6

7350×6=44100

√4410 = 210

iii ) 47068

470 68 = 2 × 2 × 7 × 41 × 41

470 68 × 7 =16900

√16900 = 130

iv) 24000

24000 =2×2×2×2×2×2×3×5×5

5×3= 15

24000 × 15 = 360000

√360000 = 600