To estimate the value of \( 6 \times \sqrt{2} \), we can first find an approximate value for \( \sqrt{2} \).
The square root of 2 is approximately 1.414. Therefore:
\[ 6 \times \sqrt{2} \approx 6 \times 1.414 = 8.484 \]
Now, rounding this to one decimal place gives us approximately 8.5. Among the choices provided:
- 8.4 (closest choice)
- 7.1
- 6.4
- 9.8
The best estimate is 8.4.