To solve this problem, we need to determine the actual rise time of the signal being measured. In oscilloscope measurements, the observed rise time (t_{\text{obs}}) is a combination of the rise time of the scope itself (t_{\text{scope}}) and the rise time of the actual signal (t_{\text{signal}}). The relation between these times can be expressed using the following formula:

t_{\text{obs}} = \sqrt{t_{\text{scope}}^2 + t_{\text{signal}}^2}

Here, we are given:

• Measured rise time, t_{\text{obs}} = 10 \, \text{ns}
• Oscilloscope rise time, t_{\text{scope}} = 6 \, \text{ns}

We need to find the actual rise time of the signal, t_{\text{signal}}. Rearranging the formula to solve for t_{\text{signal}}, we get:

t_{\text{signal}} = \sqrt{t_{\text{obs}}^2 - t_{\text{scope}}^2}

Substituting the given values:

t_{\text{signal}} = \sqrt{(10 \, \text{ns})^2 - (6 \, \text{ns})^2}

t_{\text{signal}} = \sqrt{100 \, \text{ns}^2 - 36 \, \text{ns}^2}

t_{\text{signal}} = \sqrt{64 \, \text{ns}^2}

t_{\text{signal}} = 8 \, \text{ns}

Thus, the approximate actual rise time of the signal being measured is 8 ns. This matches with the given correct answer option.