Page 63 - Start Up Mathematics_8 (Non CCE)

Example 13: 2,025 plants are to be planted in a garden in such a way that each
row contains as many plants as the rows. Find the number of rows
and the number of plants in each row? (NCERT)
Solution: Let the number of rows = x 5 2,025
\ Number of plants in each row = x 5 405
\ Total number of plants = x × x = x 2 3 81
2
According to the question, x = 2,025 3 27
3 9
3
3
fi x = 2,025 = 5 ¥ 5 ¥¥ 3 ¥¥ 3 3 3
1
= 5 × 3 × 3 = 45
So, the number of rows = 45 and the number of plants in each row = 45.
Example 14: Find the smallest number by which 8,820 should be divided to make it 2 8,820
a perfect square. Find the square root of the perfect square so obtained. 2 4,410
Solution: 8,820 = 2 × 2 × 5 × 3 × 3 × 7 × 7 5 2,205
3
441
Since 5 is left unpaired, so the smallest number by which 8,820 3 147
should be divided to make it a perfect square is 5. 7 49
\ 8,820 ÷ 5 = 1,764 7 7
1,764 = 2 × 2 × 3 × 3 × 7 × 7 1

\ 1,764 = 2 2 3 3 7 7¥ ¥ ¥ ¥ ¥

= 2 × 3 × 7

\ 1,764 = 2 × 3 × 7 = 42
Example 15: Find the smallest square number divisible by each one of the 2 6, 10, 12, 15
numbers 6, 10, 12, 15. 2 3, 5, 6, 15
Solution: LCM of 6, 10, 12, 15 = 2 × 2 × 3 × 5 = 60 3 3, 5, 3, 15

Now write 60 as a product of prime factors of the given 5 1, 5, 1, 5
numbers. 1, 1, 1, 1

So, 60 = 2 × 2 × 3 × 5
Factors 3 and 5 are left unpaired. 2 60
To make it a perfect square, we need to multiply 60 by 3 × 5. 2 30
So, 60 × (3 × 5) = 60 × 15 = 900 3 15
Hence, the smallest square number divisible by 6, 10, 12, 15 is 900. 5 5

Example 16: The product of two numbers is 256. If one number is 4 times the 1
other, find the numbers.
Solution: Product of two numbers = 256

Let one number be x. Try It Out!
256
Then the other number = Solve the given expression
x mentally.
According to the question,  25 + 49  2

256    144 
 
x = 4 ×
x
55