Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-The length of the diagonal of a box is given by $\mathrm { D } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$ where $\mathrm { L } , \mathrm { W }$, and $\mathrm { H }$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $2 \mathrm { ft }$ long, $6 \mathrm { ft }$ high, and $4 \mathrm { ft }$ wide. Give the exact value.
A) $48 \mathrm { ft }$
B) $2 \sqrt { 14 } \mathrm { ft }$
C) $12 \mathrm { ft }$
D) $4 \sqrt { 3 } \mathrm { ft }$

Question

Quizplus · Accepted Answer

Substituting $L = 2$, $W = 4$, and $H = 6$ into the formula $D = \sqrt{L^2 + W^2 + H^2}$ gives $D = \sqrt{2^2 + 4^2 + 6^2} = \sqrt{4 + 16 + 36} = \sqrt{56} = 2\sqrt{14}$ ft.

Rationalize the Denominator D=L2+W2+H2\mathrm { D } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }D=L2+W2+H2​

Rationalize the Denominator $\mathrm { D } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$