Answer :
To find which choice is equivalent to the expression [tex]\(\sqrt{20} + \sqrt{45}\)[/tex], we can simplify each square root separately.
1. Simplify [tex]\(\sqrt{20}\)[/tex]:
- We can break down 20 into 4 and 5 because [tex]\(4 \times 5 = 20\)[/tex].
- The square root of 4 is 2, so [tex]\(\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}\)[/tex].
2. Simplify [tex]\(\sqrt{45}\)[/tex]:
- We can break down 45 into 9 and 5 because [tex]\(9 \times 5 = 45\)[/tex].
- The square root of 9 is 3, so [tex]\(\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}\)[/tex].
3. Combine the simplified expressions:
- Now, we add the simplified terms: [tex]\(2\sqrt{5} + 3\sqrt{5}\)[/tex].
- Since both terms have [tex]\(\sqrt{5}\)[/tex], we can combine them: [tex]\(2\sqrt{5} + 3\sqrt{5} = (2 + 3)\sqrt{5} = 5\sqrt{5}\)[/tex].
Therefore, the expression [tex]\(\sqrt{20} + \sqrt{45}\)[/tex] simplifies to [tex]\(5\sqrt{5}\)[/tex].
So, the correct choice is C. [tex]\(5\sqrt{5}\)[/tex].
1. Simplify [tex]\(\sqrt{20}\)[/tex]:
- We can break down 20 into 4 and 5 because [tex]\(4 \times 5 = 20\)[/tex].
- The square root of 4 is 2, so [tex]\(\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}\)[/tex].
2. Simplify [tex]\(\sqrt{45}\)[/tex]:
- We can break down 45 into 9 and 5 because [tex]\(9 \times 5 = 45\)[/tex].
- The square root of 9 is 3, so [tex]\(\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}\)[/tex].
3. Combine the simplified expressions:
- Now, we add the simplified terms: [tex]\(2\sqrt{5} + 3\sqrt{5}\)[/tex].
- Since both terms have [tex]\(\sqrt{5}\)[/tex], we can combine them: [tex]\(2\sqrt{5} + 3\sqrt{5} = (2 + 3)\sqrt{5} = 5\sqrt{5}\)[/tex].
Therefore, the expression [tex]\(\sqrt{20} + \sqrt{45}\)[/tex] simplifies to [tex]\(5\sqrt{5}\)[/tex].
So, the correct choice is C. [tex]\(5\sqrt{5}\)[/tex].