Answer :
To solve the problem of determining which expressions are equal to [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex], we can follow these steps:
1. Calculate the expression [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex]:
- [tex]\(\sqrt{64} = 8\)[/tex] because [tex]\(8^2 = 64\)[/tex].
- [tex]\(\sqrt{25} = 5\)[/tex] because [tex]\(5^2 = 25\)[/tex].
- Multiply these results: [tex]\(8 \cdot 5 = 40\)[/tex].
So, [tex]\(\sqrt{64} \cdot \sqrt{25} = 40\)[/tex].
Now, let's compare this result with each option provided:
2. Compare with each option:
- Option A: [tex]\(5 \sqrt{64}\)[/tex]
- [tex]\(\sqrt{64} = 8\)[/tex], so [tex]\(5 \cdot 8 = 40\)[/tex].
- This is equal to 40, so Option A is correct.
- Option B: 40
- The number 40 matches exactly our calculated result.
- Therefore, Option B is correct.
- Option C: [tex]\(\sqrt{40}\)[/tex]
- Calculate [tex]\(\sqrt{40}\)[/tex]: This is not equal to 40 since [tex]\(\sqrt{40} \approx 6.32\)[/tex].
- Option C is not correct.
- Option D: 89
- 89 is not equal to 40.
- Option D is not correct.
- Option E: [tex]\(\sqrt{1600}\)[/tex]
- [tex]\(\sqrt{1600} = 40\)[/tex] because [tex]\(40^2 = 1600\)[/tex].
- This matches our calculated result, so Option E is correct.
- Option F: 1600
- 1600 is not equal to 40.
- Option F is not correct.
Based on our calculations, the options that are equal to [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex] are: A, B, and E.
1. Calculate the expression [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex]:
- [tex]\(\sqrt{64} = 8\)[/tex] because [tex]\(8^2 = 64\)[/tex].
- [tex]\(\sqrt{25} = 5\)[/tex] because [tex]\(5^2 = 25\)[/tex].
- Multiply these results: [tex]\(8 \cdot 5 = 40\)[/tex].
So, [tex]\(\sqrt{64} \cdot \sqrt{25} = 40\)[/tex].
Now, let's compare this result with each option provided:
2. Compare with each option:
- Option A: [tex]\(5 \sqrt{64}\)[/tex]
- [tex]\(\sqrt{64} = 8\)[/tex], so [tex]\(5 \cdot 8 = 40\)[/tex].
- This is equal to 40, so Option A is correct.
- Option B: 40
- The number 40 matches exactly our calculated result.
- Therefore, Option B is correct.
- Option C: [tex]\(\sqrt{40}\)[/tex]
- Calculate [tex]\(\sqrt{40}\)[/tex]: This is not equal to 40 since [tex]\(\sqrt{40} \approx 6.32\)[/tex].
- Option C is not correct.
- Option D: 89
- 89 is not equal to 40.
- Option D is not correct.
- Option E: [tex]\(\sqrt{1600}\)[/tex]
- [tex]\(\sqrt{1600} = 40\)[/tex] because [tex]\(40^2 = 1600\)[/tex].
- This matches our calculated result, so Option E is correct.
- Option F: 1600
- 1600 is not equal to 40.
- Option F is not correct.
Based on our calculations, the options that are equal to [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex] are: A, B, and E.
