To simplify the expression [tex]\(\sqrt{20} + \sqrt{45}\)[/tex], let's break it down into smaller steps:
1. Simplify [tex]\(\sqrt{20}\)[/tex]:
- We can factor 20 as [tex]\(4 \times 5\)[/tex].
- The square root of a product can be written as the product of the square roots: [tex]\(\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5}\)[/tex].
- Since [tex]\(\sqrt{4} = 2\)[/tex], we get [tex]\(\sqrt{20} = 2\sqrt{5}\)[/tex].
2. Simplify [tex]\(\sqrt{45}\)[/tex]:
- We can factor 45 as [tex]\(9 \times 5\)[/tex].
- Similarly, the square root of a product can be written as the product of the square roots: [tex]\(\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5}\)[/tex].
- Since [tex]\(\sqrt{9} = 3\)[/tex], we get [tex]\(\sqrt{45} = 3\sqrt{5}\)[/tex].
3. Combine the simplified expressions:
- Now we have [tex]\(\sqrt{20}\)[/tex] simplified to [tex]\(2\sqrt{5}\)[/tex] and [tex]\(\sqrt{45}\)[/tex] simplified to [tex]\(3\sqrt{5}\)[/tex].
- Adding these together: [tex]\(2\sqrt{5} + 3\sqrt{5} = (2 + 3)\sqrt{5} = 5\sqrt{5}\)[/tex].
4. Conclusion:
- The simplified expression is [tex]\(5\sqrt{5}\)[/tex].
Thus, the correct choice is:
D. [tex]\(5 \sqrt{5}\)[/tex].
