Multiply and simplify. $\sqrt { 35 } ( \sqrt { 7 } + \sqrt { 10 } )$
A) $7 \sqrt { 35 } + 5 \sqrt { 14 }$
B) $7 \sqrt { 5 } + 5 \sqrt { 7 }$
C) $7 \sqrt { 5 } + 5 \sqrt { 14 }$
D) $7 \sqrt { 10 } + 5 \sqrt { 14 }$
E) $7 \sqrt { 5 } + 5 \sqrt { 2 }$

Question

Quizplus · Accepted Answer

We can simplify the expression by distributing the square root of 35: $$\sqrt { 35 } ( \sqrt { 7 } + \sqrt { 10 } ) = \sqrt{35 \cdot 7} + \sqrt{35 \cdot 10} = \sqrt{245} + \sqrt{350}$$ We can simplify further by finding the prime factorization of 245 and 350. Note that both have a factor of 7, so we can factor out $\sqrt{7}$ from both terms: $$\sqrt{245} + \sqrt{350} = \sqrt{7\cdot 35} + \sqrt{7\cdot 50} = 7\sqrt{5} + 5\sqrt{14}$$ Therefore, the answer is choice C.

Multiply and Simplify 35(7+10)\sqrt { 35 } ( \sqrt { 7 } + \sqrt { 10 } )35​(7​+10​)

Multiply and Simplify $\sqrt { 35 } ( \sqrt { 7 } + \sqrt { 10 } )$