NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 6
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Question: 7 The students of Class VIII of a school donated 2401 in all, for 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.
Answer:
7 | 2401 |
7 | 343 |
7 | 49 |
7 | 7 |
1 |
Here, Donated money = 2401
Let the number of student be x.
Therefore donated money =
According to question,
Hence, the number of students is 49.
Question: 8 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.
Answer:
3 | 2025 |
3 | 675 |
3 | 225 |
3 | 75 |
5 | 25 |
5 | 5 |
1 |
Here, Number of plants =2025
Let the number of rows of planted plants be.
And each row contains number of plants.
According to question,
Hence, each row contains 45 plants.
Question: 9 Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
Answer:
L.C.M. of 4, 9 and 10 is 180.
2 | 180 |
2 | 90 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of
Here, prime factor 5 has no pair.
Therefore 180 must be multiplied by 5 to make it a perfect square.
Hence, the smallest square number which is divisible by 4, 9 and 10 is 900.
Question: 10. Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
Answer:
L.C.M. of 8, 15 and 20 is 120.
2 | 120 |
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of
Here, prime factor 2, 3 and 5 has no pair.
Therefore, 120 must be multiplied by to make it a perfect square.
Hence, the smallest square number which is divisible by 8, 15 and 20 is 3600.