Question

which number is closest to \\(\sqrt{67}\\) ? 7.6 9.3 8.1 8.9

Explanation:

Step1: Calculate the square of each option

• For \(7.6\): \(7.6^2 = 57.76\)
• For \(9.3\): \(9.3^2 = 86.49\)
• For \(8.1\): \(8.1^2 = 65.61\)
• For \(8.9\): \(8.9^2 = 79.21\)

Step2: Calculate the difference between each square and \(67\)

• For \(7.6\): \(|67 - 57.76| = 9.24\)
• For \(9.3\): \(|67 - 86.49| = 19.49\)
• For \(8.1\): \(|67 - 65.61| = 1.39\)
• For \(8.9\): \(|67 - 79.21| = 12.21\)

Step3: Compare the differences

The smallest difference is \(1.39\) which corresponds to \(8.1\).

Answer:

8.1