Answer :
To solve the problem of finding which option is equal to [tex]\(1.5 \sqrt{0.038}\)[/tex], let's examine each choice:
1. Calculate [tex]\(1.5 \sqrt{0.038}\)[/tex]:
- The value of [tex]\(1.5 \sqrt{0.038}\)[/tex] is approximately [tex]\(0.2924\)[/tex].
2. Evaluate each option:
- Option F: [tex]\(150 \sqrt{3.8}\)[/tex]
- This value is approximately [tex]\(292.4038\)[/tex].
- Option G: [tex]\(15 \sqrt{3.8}\)[/tex]
- This value is approximately [tex]\(29.2404\)[/tex].
- Option H: [tex]\(15 \sqrt{0.38}\)[/tex]
- This value is approximately [tex]\(9.2466\)[/tex].
- Option J: [tex]\(15 \sqrt{0.00038}\)[/tex]
- This value is approximately [tex]\(0.2924\)[/tex].
3. Comparison:
- The calculated value [tex]\(1.5 \sqrt{0.038} \approx 0.2924\)[/tex] matches with option J: [tex]\(15 \sqrt{0.00038} \approx 0.2924\)[/tex].
Therefore, the correct answer is J. [tex]\(15 \sqrt{0.00038}\)[/tex].
1. Calculate [tex]\(1.5 \sqrt{0.038}\)[/tex]:
- The value of [tex]\(1.5 \sqrt{0.038}\)[/tex] is approximately [tex]\(0.2924\)[/tex].
2. Evaluate each option:
- Option F: [tex]\(150 \sqrt{3.8}\)[/tex]
- This value is approximately [tex]\(292.4038\)[/tex].
- Option G: [tex]\(15 \sqrt{3.8}\)[/tex]
- This value is approximately [tex]\(29.2404\)[/tex].
- Option H: [tex]\(15 \sqrt{0.38}\)[/tex]
- This value is approximately [tex]\(9.2466\)[/tex].
- Option J: [tex]\(15 \sqrt{0.00038}\)[/tex]
- This value is approximately [tex]\(0.2924\)[/tex].
3. Comparison:
- The calculated value [tex]\(1.5 \sqrt{0.038} \approx 0.2924\)[/tex] matches with option J: [tex]\(15 \sqrt{0.00038} \approx 0.2924\)[/tex].
Therefore, the correct answer is J. [tex]\(15 \sqrt{0.00038}\)[/tex].
