Advertisements
Advertisements
Question
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
7688
Advertisements
Solution
Factorise each number into its prime factors.
7688 = 2 x 2 x 2 x 31 x 31
Grouping 7688 into pairs of equal factors:
7688 = (2 x 2) x (31 x 31) x 2
Here, 2 does not occur in pairs. To be a perfect square, every prime factor has to be in pairs. Hence, the smallest number by which 7688 must be multiplied is 2.
APPEARS IN
RELATED QUESTIONS
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
1458
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.
1620
By just examining the unit digit, can you tell which of the following cannot be whole square?
1024
By just examining the unit digit, can you tell which of the following cannot be whole square?
1022
Write five numbers for which you cannot decide whether they are squares.
Find the square root the following by prime factorization.
586756
By splitting into prime factors, find the square root of 194481.
Find the smallest perfect square divisible by 3, 4, 5 and 6.
Using prime factorisation, find which of the following are perfect squares.
484
Using prime factorisation, find which of the following are perfect squares.
11250
