rn 1} 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. 2} Find the smallest square number that is divisible by each of the numbers 4, 9 and 10. 3} Find the greatest 4-digit number which is a perfect square. 4} Find the length of the side of a square whose area is 441 m
2 .
rn5} A gardener has 1000 plants. He wants to plant these in such a way that the number of
rnrows and the number of columns remain same. Find the minimum number of plants he
rnneeds more for this.
rn6} There are 500 children in a school. For a P.T. drill they have to stand in such a manner
rnthat the number of rows is equal to number of columns. How many children would be left
rnout in this arrangement.
rn7} Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such
rncuboids will he need to form a cube?
1.The number of plants in each row is equal to the number of rows in the garden.
The total number of plants is 2025.
Thus, we need to find the square root of 2025
Thus the number of plants in a row is 45 and there are 45 rows in the garden.
2.Let us find the least common multiple of 4,9,10
The factorization of 4 is
The factorization of 9 is
The factorization of 10 is
Thus, the least common multiple of 4,9 and 10 is 180.
The factorization of 180 is
We know that 180 is not a perfect square.
There are two 2's and two 3's and one 5 as factors.
To get the square number we can multiply 5 to 180
We got the number 900 which is a perfect square and divisible by 4,9 and 10
3.
We need to find the greatest 4 digit number, which is a perfect square.
Greatest 4 digit number is 9999.
But 9999 is not a perfect square.
Find the approximate value of the square root of 9999.
Thus, the approximate value of the square root of 9999 is 99.999...
Now let us find the square of the number 99.
Thus the square of the number 99 is 9801.
Therefore, 9801 is the greatest 4 digit square number.