Question

which number is closest to \\(\sqrt{103}\\) ? 10.6 \quad 10.7 \quad 10.1 \quad 9.5

Explanation:

Step1: Square 10.6

$10.6^2 = 10.6 \times 10.6 = 112.36$

Step2: Square 10.7

$10.7^2 = 10.7 \times 10.7 = 114.49$

Step3: Square 10.1

$10.1^2 = 10.1 \times 10.1 = 102.01$

Step4: Square 9.5

$9.5^2 = 9.5 \times 9.5 = 90.25$

Step5: Compare to 103

Calculate differences:
$|112.36 - 103| = 9.36$
$|114.49 - 103| = 11.49$
$|102.01 - 103| = 0.99$
$|90.25 - 103| = 12.75$
The smallest difference is 0.99.

Answer:

10.1