Perform the indicated operation. Simplify, if possible. $8 \sqrt { 48 } - 5 \sqrt { 12 } + 5 \sqrt { 20 }$
A) $22 \sqrt { 3 } + 10 \sqrt { 5 }$
B) $8 \sqrt { 56 }$
C) $5 \sqrt { 3 } + 7 \sqrt { 7 }$
D) $5 \sqrt { 2 } + 7 \sqrt { 7 }$

Question

Quizplus · Accepted Answer

First, simplify each term under the square root by factoring them into prime factors or perfect squares times other integers: $8\sqrt{48} = 8\sqrt{16 \cdot 3} = 8 \cdot 4\sqrt{3} = 32\sqrt{3}$, $5\sqrt{12} = 5\sqrt{4 \cdot 3} = 5 \cdot 2\sqrt{3} = 10\sqrt{3}$, and $5\sqrt{20} = 5\sqrt{4 \cdot 5} = 5 \cdot 2\sqrt{5} = 10\sqrt{5}$. Combining like terms gives $32\sqrt{3} - 10\sqrt{3} + 10\sqrt{5} = 22\sqrt{3} + 10\sqrt{5}$.

Perform the Indicated Operation 848−512+5208 \sqrt { 48 } - 5 \sqrt { 12 } + 5 \sqrt { 20 }848​−512​+520​

Perform the Indicated Operation $8 \sqrt { 48 } - 5 \sqrt { 12 } + 5 \sqrt { 20 }$