1. **State the problem:** Simplify the expression $\left(1 - (0.6)^2\right)^{\frac{1}{2}}$. 2. **Recall the formula:** The expression is a square root of a difference, which can be written as $\sqrt{1 - (0.6)^2}$. 3. **Calculate the square inside the parentheses:** $$ (0.6)^2 = 0.36 $$ 4. **Substitute back into the expression:** $$ \sqrt{1 - 0.36} $$ 5. **Simplify inside the square root:** $$ \sqrt{0.64} $$ 6. **Calculate the square root:** $$ \sqrt{0.64} = 0.8 $$ 7. **Final answer:** $$ 0.8 $$ This means the value of $\left(1 - (0.6)^2\right)^{\frac{1}{2}}$ is $0.8$.