To estimate the value of [tex]\( 6 \times \sqrt{2} \)[/tex], we will follow these steps:
1. Approximate the value of [tex]\( \sqrt{2} \)[/tex]:
The square root of 2, [tex]\( \sqrt{2} \)[/tex], is approximately 1.414.
2. Multiply 6 by [tex]\( \sqrt{2} \)[/tex]:
We need to find the product [tex]\( 6 \times 1.414 \)[/tex].
3. Perform the multiplication:
[tex]\[
6 \times 1.414 = 8.484
\][/tex]
4. Compare the result with the given choices:
- 8.4
- 7.1
- 9.8
- 6.4
The value 8.484 is closest to 8.4 among the given choices.
Therefore, the best estimate for [tex]\( 6 \times \sqrt{2} \)[/tex] is 8.4.
