Advertisements
Advertisements
Question
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
12150
Advertisements
Solution
12150 = 2 x 3 x 3 x 3 x 3 x 3 x 5 x 5
Grouping 12150 into pairs of equal factors:
12150 = (3 x 3 x 3 x 3) x (5 x 5) x 2 x 3
Here, 2 and 3 do not occur in pairs. To be a perfect square, every prime factor has to be in pairs. Hence. the smallest number by which 12150 must be multiplied is 2 x 3, i.e. by 6.
APPEARS IN
RELATED QUESTIONS
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.
396
Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.
Find the square root the following by prime factorization.
24336
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.
Find the smallest number by which 2592 be multiplied so that the product is a perfect square.
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 cube root of 729 and 6859 prime factorisation
A square board has an area of 144 square units. How long is each side of the board?
Show that 500 is not a perfect square.
Find the smallest square number divisible by each one of the numbers 8, 9 and 10.
