Answer :

Lilith
[tex] \sqrt{63x^5y^3} \cdot \sqrt{ 14xy^8 }=\\ \\=\sqrt{63x^5y^3\cdot 14xy^8 }=\\ \\\sqrt{882x^{5+1} y^3 y^8 } =\\ \\=\sqrt{441 \cdot 2 \cdot x^6y^3y^8}=\\ \\=\sqrt{441} \cdot \sqrt{y^8}\cdot \sqrt{x^{6} }\cdot \sqrt{2y^3} = \\ \\=21 \cdot( y ^{8 })^\frac{1}{2}\cdot ( x^6)^{\frac{1}{2}}*\sqrt{2y^{3}}\\ \\=21 \cdot x^3 \cdot y^4 \cdot \sqrt{2y^3} [/tex]
[tex]\sqrt{63x^5y^3}\cdot\sqrt{14xy^8}=\sqrt{63x^5y^3\cdot14xy^8}=\sqrt{63\cdot14\cdot x^{5+1}y^{3+8}}\\\\=\sqrt{9\cdot7\cdot7\cdot2\cdot x^6y^{11}}=\sqrt9\cdot\sqrt{7^2}\cdot\sqrt{2}\cdot\sqrt{x^6}\cdot\sqrt{y^{11}}\\\\=3\cdot7\cdot\sqrt2\cdot\sqrt{(x^3)^2}\cdot\sqrt{y^{10}\cdot y}=21\sqrt2\cdot x^3\cdot\sqrt{(y^5)^2}\cdot\sqrt{y}\\\\=21x^3y^5\sqrt{2y}[/tex]

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