QuestionAugust 24, 2025

Choose all the true statements. A. sqrt (-2)=sqrt (2) B sqrt (-2)=sqrt (2i) C. sqrt (-8)=2isqrt (2) D. sqrt (-8)=-2sqrt (2) E. sqrt (-16)=4i 1F. sqrt (-16)=-4

Choose all the true statements. A. sqrt (-2)=sqrt (2) B sqrt (-2)=sqrt (2i) C. sqrt (-8)=2isqrt (2) D. sqrt (-8)=-2sqrt (2) E. sqrt (-16)=4i 1F. sqrt (-16)=-4
Choose all the true statements. A. sqrt (-2)=sqrt (2) B sqrt (-2)=sqrt (2i) C. sqrt (-8)=2isqrt (2) D. sqrt (-8)=-2sqrt (2) E. sqrt (-16)=4i 1F. sqrt (-16)=-4

Solution
4.2(256 votes)

Answer

C, E Explanation 1. Evaluate statement A \sqrt{-2} is not equal to \sqrt{2}. The square root of a negative number involves imaginary numbers. 2. Evaluate statement B \sqrt{-2} is not equal to \sqrt{2i}. Imaginary unit i should be considered separately. 3. Evaluate statement C \sqrt{-8} = \sqrt{8} \cdot i = 2\sqrt{2} \cdot i = 2i\sqrt{2}. This statement is true. 4. Evaluate statement D \sqrt{-8} does not equal -2\sqrt{2}. It involves the imaginary unit i. 5. Evaluate statement E \sqrt{-16} = \sqrt{16} \cdot i = 4 \cdot i = 4i. This statement is true. 6. Evaluate statement F \sqrt{-16} does not equal -4. It involves the imaginary unit i.

Explanation

1. Evaluate statement A<br /> $\sqrt{-2}$ is not equal to $\sqrt{2}$. The square root of a negative number involves imaginary numbers.<br />2. Evaluate statement B<br /> $\sqrt{-2}$ is not equal to $\sqrt{2i}$. Imaginary unit $i$ should be considered separately.<br />3. Evaluate statement C<br /> $\sqrt{-8} = \sqrt{8} \cdot i = 2\sqrt{2} \cdot i = 2i\sqrt{2}$. This statement is true.<br />4. Evaluate statement D<br /> $\sqrt{-8}$ does not equal $-2\sqrt{2}$. It involves the imaginary unit $i$.<br />5. Evaluate statement E<br /> $\sqrt{-16} = \sqrt{16} \cdot i = 4 \cdot i = 4i$. This statement is true.<br />6. Evaluate statement F<br /> $\sqrt{-16}$ does not equal $-4$. It involves the imaginary unit $i$.
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