multiply (radical 7) (-radical 2) give an exact answer.

Question

A. radical 5
B. - radical 14
C. radical 14
D. -7 radical 2

Answer 1

To multiply \(\sqrt{7}\) and \(-\sqrt{2}\), we can follow these steps:

\[ \sqrt{7} \cdot (-\sqrt{2}) = -(\sqrt{7} \cdot \sqrt{2}) \]

Using the property of square roots, we can combine the radicals:

\[ \sqrt{7} \cdot \sqrt{2} = \sqrt{7 \cdot 2} = \sqrt{14} \]

Thus, the multiplication becomes:

\[ -(\sqrt{14}) = -\sqrt{14} \]

So the exact answer is \(-\sqrt{14}\), which corresponds to option B:

B. - radical 14