Question

1. \\(sqrt{16b^4}\\)
2. \\(sqrt{81a^{12}d^4}\\)
3. \\(sqrt{28a^4b^3}\\)

Explanation:

Step1: Simplify $\sqrt{16b^4}$

Break into square roots: $\sqrt{16} \cdot \sqrt{b^4} = 4b^2$

Step2: Simplify $\sqrt{81a^{12}d^4}$

Break into square roots: $\sqrt{81} \cdot \sqrt{a^{12}} \cdot \sqrt{d^4} = 9a^6d^2$

Step3: Simplify $\sqrt{28a^4b^3}$

Factor into perfect squares: $\sqrt{4 \cdot 7 \cdot a^4 \cdot b^2 \cdot b} = \sqrt{4} \cdot \sqrt{a^4} \cdot \sqrt{b^2} \cdot \sqrt{7b} = 2a^2b\sqrt{7b}$

Answer:

1. $4b^2$
2. $9a^6d^2$
3. $2a^2b\sqrt{7b}$