Question

simplify. multiply and remove all perfect squares from inside the square roots. assume y is positive. \\(sqrt{12} cdot sqrt{y^3} cdot sqrt{6y} = \square\\)

Explanation:

Step1: Combine square roots

$\sqrt{12 \cdot y^3 \cdot 6y}$

Step2: Multiply inside the root

$\sqrt{72y^4}$

Step3: Factor into perfect squares

$\sqrt{36 \cdot 2 \cdot (y^2)^2}$

Step4: Extract perfect squares

$6y^2\sqrt{2}$

Answer:

$6y^2\sqrt{2}$