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Answer :
Sure, let's determine which options are equal to the expression [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex].
1. Calculate [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex]:
- [tex]\(\sqrt{64}\)[/tex] is 8 because 8 squared (8 [tex]\(\times\)[/tex] 8) equals 64.
- [tex]\(\sqrt{25}\)[/tex] is 5 because 5 squared (5 [tex]\(\times\)[/tex] 5) equals 25.
- Multiply these together: 8 [tex]\(\times\)[/tex] 5 = 40.
So, the value of the expression [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex] is 40.
2. Check each option:
- A. 1600: This is not equal to 40.
- B. [tex]\(\sqrt{1600}\)[/tex]: The square root of 1600 is 40 because 40 squared (40 [tex]\(\times\)[/tex] 40) equals 1600. So, this option is equal to 40.
- C. 40: This is exactly the same as our calculated value, so it is correct.
- D. [tex]\(5 \sqrt{64}\)[/tex]: Since [tex]\(\sqrt{64}\)[/tex] is 8, multiplying by 5 gives 5 [tex]\(\times\)[/tex] 8 = 40. This option is equal to 40.
- E. 89: This is not equal to 40.
- F. [tex]\(\sqrt{40}\)[/tex]: The square root of 40 is approximately 6.32, which is not equal to 40.
The options that are equal to [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex] are B, C, and D.
1. Calculate [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex]:
- [tex]\(\sqrt{64}\)[/tex] is 8 because 8 squared (8 [tex]\(\times\)[/tex] 8) equals 64.
- [tex]\(\sqrt{25}\)[/tex] is 5 because 5 squared (5 [tex]\(\times\)[/tex] 5) equals 25.
- Multiply these together: 8 [tex]\(\times\)[/tex] 5 = 40.
So, the value of the expression [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex] is 40.
2. Check each option:
- A. 1600: This is not equal to 40.
- B. [tex]\(\sqrt{1600}\)[/tex]: The square root of 1600 is 40 because 40 squared (40 [tex]\(\times\)[/tex] 40) equals 1600. So, this option is equal to 40.
- C. 40: This is exactly the same as our calculated value, so it is correct.
- D. [tex]\(5 \sqrt{64}\)[/tex]: Since [tex]\(\sqrt{64}\)[/tex] is 8, multiplying by 5 gives 5 [tex]\(\times\)[/tex] 8 = 40. This option is equal to 40.
- E. 89: This is not equal to 40.
- F. [tex]\(\sqrt{40}\)[/tex]: The square root of 40 is approximately 6.32, which is not equal to 40.
The options that are equal to [tex]\(\sqrt{64} \cdot \sqrt{25}\)[/tex] are B, C, and D.
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