Perform the operation and write the result in standard form. − 28 + − 112 \sqrt { - 28 } + \sqrt { - 112 } − 28 + − 112 A) 9 i 7 9 i \sqrt { 7 } 9 i 7 B) 11 i 7 \sqrt { 11 } i \sqrt { 7 } 11 i 7 C) − 5 i 7 - 5 i \sqrt { 7 } − 5 i 7 D) 6 i 7 6 i \sqrt { 7 } 6 i 7 E) − 2 i 7 - 2 i \sqrt { 7 } − 2 i 7

Question

Perform the operation and write the result in standard form.   − 28 + − 112 \sqrt { - 28 } + \sqrt { - 112 } − 28 ​ + − 112 ​ A)    9 i 7 9 i \sqrt { 7 } 9 i 7 ​ B)    11 i 7 \sqrt { 11 } i \sqrt { 7 } 11 ​ i 7 ​ C)    − 5 i 7 - 5 i \sqrt { 7 } − 5 i 7 ​ D)    6 i 7 6 i \sqrt { 7 } 6 i 7 ​ E)    − 2 i 7 - 2 i \sqrt { 7 } − 2 i 7 ​

Jekemea Hunter · Accepted Answer

Final Answer : D, Explanation :   We can first simplify both square roots by factoring out the greatest perfect square factor from each of them: − 28 + − 112 = − 4 ⋅ 7 + − 16 ⋅ 7 = 2 i 7 + 4 i 7 = 6 i 7 \sqrt{-28}+\sqrt{-112}=\sqrt{-4\cdot7}+\sqrt{-16\cdot7}=2i\sqrt{7}+4i\sqrt{7}=6i\sqrt{7} − 28 ​ + − 112 ​ = − 4 ⋅ 7 ​ + − 16 ⋅ 7 ​ = 2 i 7 ​ + 4 i 7 ​ = 6 i 7 ​ Therefore, the answer is choice D.

Perform the operation and write the result in standard form. $−28+−112\sqrt { - 28 } + \sqrt { - 112 }$

A) $\sqrt { 7 }$
B) $11i7\sqrt { 11 } i \sqrt { 7 }$
C) $\sqrt { 7 }$
D) $\sqrt { 7 }$
E) $\sqrt { 7 }$

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Perform the operation and write the result in standard form. −28+−112\sqrt { - 28 } + \sqrt { - 112 }−28​+−112​ A) 9i79 i \sqrt { 7 }9i7​ B) 11i7\sqrt { 11 } i \sqrt { 7 }11​i7​ C) −5i7- 5 i \sqrt { 7 }−5i7​ D) 6i76 i \sqrt { 7 }6i7​ E) −2i7- 2 i \sqrt { 7 }−2i7​

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Learning Objectives

Learning Objectives

Related questions

Perform the operation and write the result in standard form. $−28+−112\sqrt { - 28 } + \sqrt { - 112 }$

A) $\sqrt { 7 }$
B) $11i7\sqrt { 11 } i \sqrt { 7 }$
C) $\sqrt { 7 }$
D) $\sqrt { 7 }$
E) $\sqrt { 7 }$