Question

use the calculator below to approximate \\(\sqrt{68}\\) as a decimal to the tenths place. note that you must do the approximation without using a square root button. your answer must be within a tenth of the actual value.

Explanation:

Step1: Identify nearest perfect squares

We know $8^2=64$ and $9^2=81$, so $\sqrt{68}$ is between 8 and 9.

Step2: Test 8.2, calculate its square

$8.2^2 = 8.2 \times 8.2 = 67.24$

Step3: Test 8.3, calculate its square

$8.3^2 = 8.3 \times 8.3 = 68.89$

Step4: Compare to 68

$67.24 < 68 < 68.89$. 68 is closer to 67.24 than 68.89? No, $68-67.24=0.76$, $68.89-68=0.89$. So 8.2 is closer, but we check tenths place requirement.

Answer:

8.2