The length of a rectangular prism is 4√3 units. The height is 3√6 units. If the volume is irrational, which could be the measure of the width of the rectangular prism? Answer choices:A. 2√50B. 4√12C. 5√8D. 7√18 PLEASE EXPLAIN ALL STEPS
Accepted Solution
A:
volume = length * height * width = 4 qrt3 + 3 sqrt6 * w = 12 sqrt18 w
let w = 2 sqrt50 then volume = 2*12 * sqrt 18*50 = 24*30 so this is rational
let w = 4 sqt 12 the v = 48 sqrt12 * sqrt 18 = 48 sqrt30 which is irrational