Homework Help

Find the least divisor of 2744 which would make the quotient a perfect square.

user profile pic

shewa55 | (Level 1) Valedictorian

Posted May 6, 2013 at 4:25 PM via web

dislike 1 like

Find the least divisor of 2744 which would make the quotient a perfect square.

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 6, 2013 at 4:37 PM (Answer #1)

dislike 1 like

You need to use the following relations between the numbers `x,y` , provided by the problem, such that:

`{(2744/x = y),(x^2 = y):} => {(2744/x = x^2),(x^2 = y):} =>2744 = x^3`

`x = root(3) 2744 => x = 14 => y = 14^2 => y = 196`

Hence, evaluating the numbers x,y, under the given conditions, yields `x = 14, y = 196.`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes