Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The prime factorisation of 180:
180 = 2 x 2 x 3 x 3 x 5
Grouping the factors into pairs of equal factors, we get:
180 = (2 x 2) x (3 x 3) x 5
The factor, 5 does not have a pair. Therefore, we must multiply 180 by 5 to make a perfect square. The new number is:
(2 x 2) x (3 x 3) x (5 x 5) = 900
Taking one factor from each pair on the LHS, the square root of the new number is 2 x 3 x 5, which is equal to 30.
APPEARS IN
संबंधित प्रश्न
Find the square root of the following number by the prime factorisation method.
9604
Find the square root of the following number by the prime factorisation method.
9216
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:
1800
By just examining the unit digit, can you tell which of the following cannot be whole square?
1022
Find the square root the following by prime factorization.
4096
A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 71 were left out after arrangement.
Examine if the following is a perfect square
190
Find the square root by prime factorisation method
9025
1000 is a perfect square.
