The smallest number by which 6000 should be divided to get a Perfect square number is

The prime factorization of 2400 =(2 × 2) × (2 × 2) × 2 × (5 × 5) × 3

∴ 2,3 are needed to form a pair 

∴ 2 × 3 = 6 

∴ 6 should be multiplied with 2400 then we will get a perfect square number. 

∴ 2400 × 6 = 14400

∴ \(\sqrt {14400}\) = 120

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Solution

The correct option is D 66000 = 2×2×2×5×5×5×6 Hence, the factor 6 does not appear in the group of three So, if we divide the number by 6, then the quotient will be perfect cube. 60006=1000 which is a perfect cube.

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620

Solution:

We have to find the smallest whole number by which the number should be divided so as to get a perfect square number

To get a perfect square, each factor of the given number must be paired.

(i) 252

Hence, prime factor 7 does not have its pair. If the number is divided by 7, then the rest of the prime factor will be in pairs. Therefore, 252 has to be divided by 7 to get a perfect square.

252 ÷ 7 = 36

36 is perfect square

36 = 2 × 2 × 3 × 3

= 22 × 32

= (2 × 3)2

Thus, √36 = 2 × 3 = 6

(ii) 2925

Hence, prime factor 13 does not have its pair. If the number is divided by 13, then the rest of the prime factor will be in pairs. Therefore, 2925 has to be divided by 13 to get a perfect square.

2925 ÷ 13 = 225

225 is a perfect square

225 = 5 × 5 × 3 × 3

= 52 × 32

= (5 × 3)2

Thus, √225 = 15

(iii) 396

Hence, prime factor 11 does not have its pair. If the number is divided by 11, then the rest of the prime factor will be in pairs.

Therefore, 396 has to be divided by 11 to get a perfect square.

396 ÷ 11 = 36

36 is a perfect square

36 = 3 × 3 × 2 × 2

= 32 × 22

= (3 × 2)2

Thus, √36 = 3 × 2 = 6

(iv) 2645

Hence, prime factor 5 does not have its pair. If the number is divided by 5, then the rest of the prime factor will be in pairs.

Therefore, 2645 has to be divided by 5 to get a perfect square.

2645 ÷ 5 = 529

529 is a perfect square

529 = 23 × 23

= 232

Thus, √529 = 23

(v) 2800

Hence, prime factor 7 does not have its pair. If the number is divided by 7, then the rest of the prime factor will be in pairs. Therefore, 2800 has to be divided by 7 to get a perfect square

2800 ÷ 7 = 400

400 is a perfect square

400 = 2 × 2 × 2 × 2 × 5 × 5

= 22 × 22 × 52

= (2 × 3 × 5)2

Thus, √400 = 2 × 2 × 5 = 20

(vi) 1620

Hence, prime factor 5 does not have its pair. If the number is divided by 5, then the rest of the prime factor will be in pairs.

Therefore, 1620 has to be divided by 5 to get a perfect square.

1620 ÷ 5 = 324

324 is a perfect square

324 = 2 × 2 × 3 × 3 × 3 × 3

= 22 × 32 × 32

= (2 × 3 × 3)2

Thus, √324 = 2 × 3 × 3 = 18

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

Video Solution:

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.3 Question 6

Summary:

For each of the following numbers (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620, the smallest whole number by which it should be divided so as to get a perfect square and the square root of the square numbers are as follows (i) 7; √36 = 6 (ii) 13; √225 = 15 (iii) 11; √36 = 6 (iv) 5; √529 = 23 (v) 7; √400 = 20 and (vi) 5; √324 = 18

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