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
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.
2645
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 units digit, can you tell which of the following cannot be whole square?
1026
By just examining the unit digit, can you tell which of the following cannot be whole square?
1023
Write five numbers which you cannot decide whether they are square just by looking at the unit's digit.
Find the square root the following by prime factorization.
190969
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.
Out of 745 students, maximum are to be arranged in the school field for a P.T. display, such that the number of rows is equal to the number of columns. Find the number of rows if 16 students were left out after the arrangement.
Find the square root by prime factorisation method
4761
Find the smallest square number divisible by each one of the numbers 8, 9 and 10.
