Answer :
To solve the problem, we'll simplify each square root separately and then combine the results.
1. Simplify [tex]\(\sqrt{45}\)[/tex]:
- Break down 45 into its factors: [tex]\(45 = 9 \times 5\)[/tex].
- Since 9 is a perfect square, we can take the square root of 9: [tex]\(\sqrt{9} = 3\)[/tex].
- This gives us: [tex]\(\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}\)[/tex].
2. Simplify [tex]\(\sqrt{125}\)[/tex]:
- Break down 125 into its factors: [tex]\(125 = 25 \times 5\)[/tex].
- Since 25 is a perfect square, we can take the square root of 25: [tex]\(\sqrt{25} = 5\)[/tex].
- This gives us: [tex]\(\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}\)[/tex].
3. Combine the simplified square roots:
- Now we can add the simplified square roots: [tex]\(3\sqrt{5} + 5\sqrt{5}\)[/tex].
- Since both terms are in terms of [tex]\(\sqrt{5}\)[/tex], we add the coefficients: [tex]\(3 + 5 = 8\)[/tex].
- Thus, we have: [tex]\(8\sqrt{5}\)[/tex].
So, the expression [tex]\(\sqrt{45} + \sqrt{125}\)[/tex] simplifies to [tex]\(8\sqrt{5}\)[/tex]. Therefore, the correct choice is A. [tex]\(8 \sqrt{5}\)[/tex].
1. Simplify [tex]\(\sqrt{45}\)[/tex]:
- Break down 45 into its factors: [tex]\(45 = 9 \times 5\)[/tex].
- Since 9 is a perfect square, we can take the square root of 9: [tex]\(\sqrt{9} = 3\)[/tex].
- This gives us: [tex]\(\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}\)[/tex].
2. Simplify [tex]\(\sqrt{125}\)[/tex]:
- Break down 125 into its factors: [tex]\(125 = 25 \times 5\)[/tex].
- Since 25 is a perfect square, we can take the square root of 25: [tex]\(\sqrt{25} = 5\)[/tex].
- This gives us: [tex]\(\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}\)[/tex].
3. Combine the simplified square roots:
- Now we can add the simplified square roots: [tex]\(3\sqrt{5} + 5\sqrt{5}\)[/tex].
- Since both terms are in terms of [tex]\(\sqrt{5}\)[/tex], we add the coefficients: [tex]\(3 + 5 = 8\)[/tex].
- Thus, we have: [tex]\(8\sqrt{5}\)[/tex].
So, the expression [tex]\(\sqrt{45} + \sqrt{125}\)[/tex] simplifies to [tex]\(8\sqrt{5}\)[/tex]. Therefore, the correct choice is A. [tex]\(8 \sqrt{5}\)[/tex].