NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 6

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Image shows find Square root using 2 methods

Image Shows Find Square Root Using 2 Methods

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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:

A table shows the factor of 2401 to find smallest square number

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:

A table shows the factor of 2025 to find smallest square number

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.

A table shows the factor of 180 to find smallest square number

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.

A table shows the factor of 120 to find smallest square number

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.