Questions: Which of the following is equivalent to √20-3 √5+2 √45 ? 17 √5 5 √5 7 √5 19 √5

Solution Steps

To solve the expression \(\sqrt{20} - 3 \sqrt{5} + 2 \sqrt{45}\), we need to simplify each square root term and then combine like terms.

1. Simplify \(\sqrt{20}\) to \(2 \sqrt{5}\).
2. Simplify \(\sqrt{45}\) to \(3 \sqrt{5}\).
3. Substitute these simplified forms back into the expression.
4. Combine the like terms involving \(\sqrt{5}\).

\[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \]

\[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \]

Substitute the simplified forms back into the expression: \[ 2\sqrt{5} - 3\sqrt{5} + 2 \times 3\sqrt{5} \]

Combine the like terms: \[ 2\sqrt{5} - 3\sqrt{5} + 6\sqrt{5} = (2 - 3 + 6)\sqrt{5} = 5\sqrt{5} \]

Final Answer