Question

-5 squareroot 7 + 7 squareroot 28

Answer 1

To simplify the expression \(-5\sqrt{7} + 7\sqrt{28}\), we start by simplifying \(\sqrt{28}\).

We know that:

\[
\sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7}
\]

Now we can substitute \(\sqrt{28}\) with \(2\sqrt{7}\) in the expression:

\[
-5\sqrt{7} + 7\sqrt{28} = -5\sqrt{7} + 7(2\sqrt{7})
\]

Now, let's simplify this further:

\[
= -5\sqrt{7} + 14\sqrt{7}
\]

Next, we can combine the like terms:

\[
= (-5 + 14)\sqrt{7} = 9\sqrt{7}
\]

Thus, the simplified form of the expression is:

\[
\boxed{9\sqrt{7}}
\]