Advertisements
Advertisements
Question
Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.
Advertisements
Solution
The prime factorisation of 147:
147 = 3 x 7 x 7
Grouping the factors into pairs of equal factors, we get:
147 = 3 x (7 x 7)
The factor, 3 does not have a pair. Therefore, we must multiply 147 by 3 to make a perfect square. The new number is:
(3 x 3) x (7 x 7) = 441
Taking one factor from each pair on the LHS, the square root of the new number is 3 x 7, which is equal to 21.
APPEARS IN
RELATED QUESTIONS
Find the square root of the following number by the prime factorisation method.
8100
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
Write five numbers for which you cannot decide whether they are squares.
Find the square root the following by prime factorization.
529
Find the smallest perfect square divisible by 3, 4, 5 and 6.
Find the square root by prime factorisation method
784
If `root(3)(1906624) xx sqrt(x)` = 3100, find x
Using prime factorisation, find which of the following are perfect squares.
11250
Using prime factorisation, find the square roots of 11025
