Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement.
-$64 a \sqrt { d } + 64 a$
A) $8 \sqrt { a } ( 8 \sqrt { 11 } + \sqrt { d } )$
B) $\sqrt { 11 a } ( 64 \sqrt { d } - 8 \sqrt { 7 } )$
C) $8 \sqrt { a } ( 8 \sqrt { a d } + 8 \sqrt { a } )$
D) $\sqrt { 7 d } \left( \sqrt { 1,331 a d } + \sqrt { 605 d ^ { 2 } } \right)$

Question

Find the following products and express answers in simplest radical form. All variables represent non negative real numbers. Match each of the expressions with the expression to obtain a true statement.
-$64 a \sqrt { d } + 64 a$ 
A) $8 \sqrt { a } ( 8 \sqrt { 11 } + \sqrt { d } )$ 
B) $\sqrt { 11 a } ( 64 \sqrt { d } - 8 \sqrt { 7 } )$ 
C) $8 \sqrt { a } ( 8 \sqrt { a d } + 8 \sqrt { a } )$ 
D) $\sqrt { 7 d } \left( \sqrt { 1,331 a d } + \sqrt { 605 d ^ { 2 } } \right)$

Quizplus · Accepted Answer

Factor out 64a to get $64a(\sqrt{d}+1)$. Then, we can simplify $\sqrt{a}\cdot\sqrt{ad}=\sqrt{a^2d}$ to get $8\sqrt{a}(8\sqrt{ad}+8a)$. This matches choice C.

Find the Following Products and Express Answers in Simplest Radical 64ad+64a64 a \sqrt { d } + 64 a64ad​+64a

Find the Following Products and Express Answers in Simplest Radical $64 a \sqrt { d } + 64 a$