Advertisements
Advertisements
प्रश्न
Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
Advertisements
उत्तर
The prime factorisation of 3645:
3645 = 3 x 3 x 3 x 3 x 3 x 3 x 5
Grouping the factors into pairs of equal factors, we get:
3645 = (3 x 3) x (3 x 3) x (3 x 3) x 5
The factor, 5 does not have a pair. Therefore, we must divide 3645 by 5 to make a perfect square. The new number is:
(3 x 3) x (3 x 3) x (3 x 3) = 729
Taking one factor from each pair on the LHS, the square root of the new number is 3 x 3 x 3, which is equal to 27.
APPEARS IN
संबंधित प्रश्न
Find the square root of the following number by the prime factorisation method.
529
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
252
Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.
By just examining the unit digit, can you tell which of the following cannot be whole square?
1023
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
25
Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also, find the square root of the number so obtained.
The students of class VIII of a school donated Rs 2401 for PM'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.
By splitting into prime factors, find the square root of 396900.
Examine if the following is a perfect square
725
Find the square root by prime factorisation method
256
