-4 squareroot 63 + 9 squareroot 7

1 answer

To simplify the expression \(-4\sqrt{63} + 9\sqrt{7}\), we first simplify \(\sqrt{63}\).

\[ \sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \]

Now, we can substitute \(\sqrt{63}\) in the original expression:

\[ -4\sqrt{63} + 9\sqrt{7} = -4(3\sqrt{7}) + 9\sqrt{7} \]

This simplifies to:

\[ -12\sqrt{7} + 9\sqrt{7} \]

Now, we can combine the terms:

\[ (-12 + 9)\sqrt{7} = -3\sqrt{7} \]

Thus, the final simplified expression is:

\[ \boxed{-3\sqrt{7}} \]