Question

7. 3sqrt(5) - 2sqrt(20)

Answer 1

To simplify the expression \( 3\sqrt{5} - 2\sqrt{20} \), we can start by simplifying \( \sqrt{20} \).

We know that:
\[
\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}
\]

Now we can substitute this back into the expression:
\[
3\sqrt{5} - 2\sqrt{20} = 3\sqrt{5} - 2(2\sqrt{5}) = 3\sqrt{5} - 4\sqrt{5}
\]

Now, we can combine the like terms:
\[
3\sqrt{5} - 4\sqrt{5} = (3 - 4)\sqrt{5} = -1\sqrt{5} = -\sqrt{5}
\]

Thus, the simplified expression is:
\[
-\sqrt{5}
\]