If n is the smallest integer such that 108 times n is the square of an integer, what is the value of...
If n is the smallest integer such that 108 times n is the square of an integer, what is the value of n?
Answer/Solution
2
Steps/Work
108 can written as = 2 * 2 * 3 * 3 * 3 --> 2^2* 3^3 ---(1)
so for 108 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.
here 2 already has even power -> So n has to be 2 to make the power of 2 in (1) even
Option A is correct
so for 108 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.
here 2 already has even power -> So n has to be 2 to make the power of 2 in (1) even
Option A is correct