Questions: Simplify. -√45-4 √20

Solution Steps

To simplify the expression \(-\sqrt{45} - 4\sqrt{20}\), we first need to simplify each square root term by factoring out perfect squares. Then, we combine like terms if possible.

We start with the term \(-\sqrt{45}\). We can factor \(45\) as \(9 \times 5\), where \(9\) is a perfect square. Thus, we have: \[ -\sqrt{45} = -\sqrt{9 \times 5} = -\sqrt{9} \cdot \sqrt{5} = -3\sqrt{5} \]

Next, we simplify the term \(-4\sqrt{20}\). We can factor \(20\) as \(4 \times 5\), where \(4\) is a perfect square. Therefore, we have: \[ -4\sqrt{20} = -4\sqrt{4 \times 5} = -4\sqrt{4} \cdot \sqrt{5} = -4 \cdot 2\sqrt{5} = -8\sqrt{5} \]

Now we combine the simplified terms: \[ -\sqrt{45} - 4\sqrt{20} = -3\sqrt{5} - 8\sqrt{5} = (-3 - 8)\sqrt{5} = -11\sqrt{5} \]

Final Answer