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
☛ Related Questions:
- The students of Class VIII of a school donated ₹ 2401 in all for the Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
- 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
- Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
- Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.