Answer :
Final answer:
The expression equivalent to \(\sqrt{20} + \sqrt{45}\) is simplified by factoring out the perfect squares within the radicals, resulting in \(5\sqrt{5}\).
Explanation:
To find an expression equivalent to \(\sqrt{20} + \sqrt{45}\), we need to simplify each radical. Since both 20 and 45 have perfect squares as factors, we can break them down:
- \(\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}\)
- \(\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}\)
Now we can combine these terms since they have the same radical part:
\(2\sqrt{5} + 3\sqrt{5} = (2+3)\sqrt{5} = 5\sqrt{5}\)
Therefore, the expression that is equivalent to \(\sqrt{20} + \sqrt{45}\) is \(5\sqrt{5}\).
Answer :
→ √20 + √45
→ 2√5 + 3√5
- Taking √5 as common.
→ (2 + 3)√5
→ 5√5
Therefore, option A is correct.