Question

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√50
B. 4√12
C. 5√8
D. 7√18 PLEASE EXPLAIN ALL STEPS

Answer 1

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

C and D are rational  
answer is B