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.
9604
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 number by which the given number must be divided so that the resulting number is a perfect square:
14283
By just examining the unit digit, can you tell which of the following cannot be whole square?
1022
By just examining the unit digit, can you tell which of the following cannot be whole square?
1023
Write true (T) or false (F) for the following statement.
The sum of two square numbers is a square number.
Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.
The area of a square field is 5184 cm2. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.
Write the prime factorization of the following number and hence find their square root.
9604
Find the smallest perfect square divisible by 3, 4, 5 and 6.
