Question

1. $3sqrt3{5y^{3}}cdot2sqrt3{50y^{4}}$

Explanation:

Step1: Multiply coefficients

$3 \times 2 = 6$

Step2: Combine radicands

$\sqrt[3]{5y^3 \cdot 50y^4} = \sqrt[3]{250y^7}$

Step3: Simplify radicand

$250y^7 = 5^3 \cdot 2 \cdot (y^2)^3 \cdot y = (5y^2)^3 \cdot 2y$

Step4: Extract cube root

$\sqrt[3]{(5y^2)^3 \cdot 2y} = 5y^2\sqrt[3]{2y}$

Step5: Multiply results

$6 \cdot 5y^2\sqrt[3]{2y} = 30y^2\sqrt[3]{2y}$

Answer:

$30y^2\sqrt[3]{2y}$