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

Question

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

Zybrea Knight · Accepted Answer

Final Answer : C, Explanation :   We can simplify the expression by distributing the square root of 35:   35 ( 7 + 10 ) = 35 ⋅ 7 + 35 ⋅ 10 = 245 + 350 \sqrt { 35 } ( \sqrt { 7 } + \sqrt { 10 } ) = \sqrt{35 \cdot 7} + \sqrt{35 \cdot 10} = \sqrt{245} + \sqrt{350} 35 ​ ( 7 ​ + 10 ​ ) = 35 ⋅ 7 ​ + 35 ⋅ 10 ​ = 245 ​ + 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   7 \sqrt{7} 7 ​   from both terms:   245 + 350 = 7 ⋅ 35 + 7 ⋅ 50 = 7 5 + 5 14 \sqrt{245} + \sqrt{350} = \sqrt{7\cdot 35} + \sqrt{7\cdot 50} = 7\sqrt{5} + 5\sqrt{14} 245 ​ + 350 ​ = 7 ⋅ 35 ​ + 7 ⋅ 50 ​ = 7 5 ​ + 5 14 ​   Therefore, the answer is choice C.

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

A) $\sqrt { 35 } + 5 \sqrt { 14 }$
B) $\sqrt { 5 } + 5 \sqrt { 7 }$
C) $\sqrt { 5 } + 5 \sqrt { 14 }$
D) $\sqrt { 10 } + 5 \sqrt { 14 }$
E) $\sqrt { 5 } + 5 \sqrt { 2 }$

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