Perform the indicated operation. Assume that all variables represent positive real numbers.
-$( \sqrt { 6 } - 3 ) ( \sqrt { 5 } - 6 )$
A) $\sqrt { 30 } + 18$
B) $\sqrt { 30 } - 6 \sqrt { 6 } - 3 \sqrt { 5 } + 18$
C) $- 8 \sqrt { 30 } + 18$
D) $\sqrt { 30 } - 9 \sqrt { 5 } + 18$

Question

Quizplus · Accepted Answer

To solve $( \sqrt { 6 } - 3 ) ( \sqrt { 5 } - 6 )$, we use the distributive property (FOIL method): $\sqrt{6} \cdot \sqrt{5} + \sqrt{6} \cdot (-6) + (-3) \cdot \sqrt{5} + (-3) \cdot (-6)$. This simplifies to $\sqrt{30} - 6\sqrt{6} - 3\sqrt{5} + 18$.

Perform the Indicated Operation (6−3)(5−6)( \sqrt { 6 } - 3 ) ( \sqrt { 5 } - 6 )(6​−3)(5​−6)

Perform the Indicated Operation $( \sqrt { 6 } - 3 ) ( \sqrt { 5 } - 6 )$