Question
Estimate the value of 6 times the square root of 2. Which of the following choices is the best estimate?
A. 6.4
B. 7.1
C. 9.8
D. 8.4
A. 6.4
B. 7.1
C. 9.8
D. 8.4
Answers
GPT-4o mini
To estimate the value of \( 6 \times \sqrt{2} \), we first need an approximate value for \( \sqrt{2} \). We know that:
\[
\sqrt{2} \approx 1.414
\]
Now, we calculate:
\[
6 \times \sqrt{2} \approx 6 \times 1.414
\]
Calculating this gives:
\[
6 \times 1.414 = 8.484
\]
Now we compare this value to the options provided:
A. 6.4
B. 7.1
C. 9.8
D. 8.4
The closest estimate to \( 8.484 \) is:
**D. 8.4**
\[
\sqrt{2} \approx 1.414
\]
Now, we calculate:
\[
6 \times \sqrt{2} \approx 6 \times 1.414
\]
Calculating this gives:
\[
6 \times 1.414 = 8.484
\]
Now we compare this value to the options provided:
A. 6.4
B. 7.1
C. 9.8
D. 8.4
The closest estimate to \( 8.484 \) is:
**D. 8.4**