Perform the indicated operations. Assume that all variables represent positive numbers.
-$\sqrt { 7 } ( \sqrt { 28 } + \sqrt { 14 } )$
A) $14 + 7 \sqrt { 2 }$
B) $14 + 49 \sqrt { 2 }$
C) 28
D) $196 + 7 \sqrt { 2 }$

Question

Quizplus · Accepted Answer

First, simplify inside the parentheses: $\sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7}$ and $\sqrt{14} = \sqrt{2 \cdot 7} = \sqrt{2}\sqrt{7}$. So, the expression becomes $\sqrt{7}(2\sqrt{7} + \sqrt{2}\sqrt{7})$. Factoring out $\sqrt{7}$, we get $\sqrt{7} \cdot 2\sqrt{7} + \sqrt{7} \cdot \sqrt{2}\sqrt{7} = 2 \cdot 7 + 7\sqrt{2} = 14 + 7\sqrt{2}$.

Perform the Indicated Operations 7(28+14)\sqrt { 7 } ( \sqrt { 28 } + \sqrt { 14 } )7​(28​+14​)

Perform the Indicated Operations $\sqrt { 7 } ( \sqrt { 28 } + \sqrt { 14 } )$