Question

1. simplify.

$5\sqrt{18x^{6}} + 8\sqrt{48x^{2}y^{2}} + 6\sqrt{50xy^{2}}$
$\bigcirc$ $77xy\sqrt{2}$
$\bigcirc$ $15x^{2}\sqrt{2} + 32y\sqrt{3x} + 30y\sqrt{2x}$
$\bigcirc$ $15x^{3}\sqrt{2} + 32xy\sqrt{3} + 30y\sqrt{2x}$
$\bigcirc$ $5x^{3}\sqrt{2} + 16xy\sqrt{3}$

Explanation:

Step1: Simplify first radical

$5\sqrt{18x^6}=5\sqrt{9x^6 \cdot 2}=5 \cdot 3x^3\sqrt{2}=15x^3\sqrt{2}$

Step2: Simplify second radical

$8\sqrt{48x^2y^2}=8\sqrt{16x^2y^2 \cdot 3}=8 \cdot 4xy\sqrt{3}=32xy\sqrt{3}$

Step3: Simplify third radical

$6\sqrt{50xy^2}=6\sqrt{25y^2 \cdot 2x}=6 \cdot 5y\sqrt{2x}=30y\sqrt{2x}$

Step4: Combine all terms

$15x^3\sqrt{2} + 32xy\sqrt{3} + 30y\sqrt{2x}$

Answer:

15$x^3\sqrt{2} + 32xy\sqrt{3} + 30y\sqrt{2x}$