Question

simplify. remove all perfect squares from inside the square root. assume b is positive. \\(sqrt{48b^7} = \square\\)

Explanation:

Step1: Factor into perfect squares

$\sqrt{16 \times 3 \times b^6 \times b}$

Step2: Split square root into products

$\sqrt{16} \times \sqrt{3} \times \sqrt{b^6} \times \sqrt{b}$

Step3: Simplify perfect square roots

$4 \times \sqrt{3} \times b^3 \times \sqrt{b}$

Step4: Combine remaining radicals

$4b^3\sqrt{3b}$

Answer:

$4b^3\sqrt{3b}$