The largest 4 digit number which is exactly divisible by 18, 25 and 35. Find the smallest number by which 1008 must be. multiplied to get a perfect square. Also find the square root of square so obtained. 1225 plants are to be planted in a garden is 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.
18 = 2*3*3
25 = 5*5
35 = 5*7
LCM = 2*3*3*5*5*7 = 3150
how about 3150k < 9999
k < 3.1
so largest 4 digit with above properties is 3*3150 = 9450
test it with your calculator.
1008 = 2*2*2*2*3*3*7
= 16 * 9 * 7
the first two factors are perfect square, so to make the last factor a perfect square, we have to multiply by 7
so 1008*7 = 7056
check: √7056 = 84
take a run at the last one, let me know what you think.
To find the largest 4-digit number that is divisible by 18, 25, and 35, we need to find the least common multiple (LCM) of these three numbers.
Step 1: Find the LCM of 18, 25, and 35.
To find the LCM, we can use prime factorization:
18 = 2 * 3^2
25 = 5^2
35 = 5 * 7
To find the LCM, we need to take the highest power of each prime factor:
LCM = 2 * 3^2 * 5^2 * 7 = 3150
So, the largest 4-digit number that is divisible by 18, 25, and 35 is 3150.
To find the smallest number by which 1008 must be multiplied to get a perfect square, we need to factorize 1008 and check for the missing factors of 2.
Step 2: Factorize 1008.
1008 = 2^4 * 3^2 * 7
To make it a perfect square, we need to find the smallest number that will complete the missing factors of 2. Since the power of 2 is already 4, we need 2^2 (to complete power of 2 to 6).
Therefore, the number we need is 2^2 = 4.
Step 3: Multiply 1008 by 4 to get a perfect square.
1008 * 4 = 4032
To find the square root of 4032, we can use a calculator or approximate it.
√4032 ≈ 63.5
Therefore, the square root of the square obtained (4032) is approximately 63.5.
In the garden, there are 1225 plants to be planted in such a way that each row contains as many plants as the number of rows.
Step 4: Find the number of rows and the number of plants in each row.
To find the number of rows, we need to find the square root of the total number of plants (1225).
√1225 = 35
So, the number of rows is 35.
Since each row contains as many plants as the number of rows, the number of plants in each row is also 35.
Therefore, there are 35 rows and 35 plants in each row in the garden.