Question

$\sqrt[3]{3x+\sqrt[3]{3x^{2}y}+3\sqrt[3]{3x{y}^2}+y}=$______________

• A. $(\sqrt{x}+\sqrt{y})$
• B. $(\sqrt{x}-\sqrt{y})$
• C. $(\sqrt[3]{3x}+\sqrt[3]{3y})$
• D. $(\sqrt{x}+\sqrt[3]{3y})$

Answer 1

The correct option is A $(\sqrt{x}+\sqrt{y})$

Given epression is

$(x+3(x^{2}y{)}^{\frac{1}{3}}+3(x{y}^2{)}^{\frac{1}{3}}+y{)}^{\frac{1}{3}}$

$\left[\right(x^{\frac{1}{3}}{)}^3+(y^{\frac{1}{3}}{)}^3+3\times x^{\frac{2}{3}}\times y^{\frac{1}{3}}+3\times x^{\frac{1}{3}}\times y^{\frac{2}{3}}{]}^{\frac{1}{3}}$

$⟹\left(\right(x^{\frac{1}{3}}+y^{\frac{1}{3}}{)}^3{)}^{\frac{1}{3}}$

$⟹(x^{\frac{1}{3}}+y^{\frac{1}{3}})$

$⟹(\sqrt{x}+\sqrt{y})$