Question

What is the following sum 2{^3 square root 16x^3y}+4{^3 square root 54x^6y^5}?

Answer 1

$2\sqrt[3]{16x^{3}y}+4\sqrt[3]{54x^{6}y^5}}=2\sqrt[3]{(2x)^{3}\cdot 2y}+4\sqrt[3]{(3x^{2}y)^{3}\cdot 2y^{2}}\\\\=4x\sqrt[3]{2y}+12x^{2}\sqrt[3]{2y^{2}}$

Answer 2

Answer:

$4x\sqrt[3]{2y}$ +$12x^2y\sqrt[3]{2y^2}$

Step-by-step explanation:

Given expression $3\sqrt[3]{16x^3y} + 4\sqrt[3]{54x^6y^5}$.

Let us simplify each of the radical separately first.

$3\sqrt[3]{16x^3y}=3\sqrt[3]{2\times 8 \times x^3\times y} =2\sqrt[3]{2} \times \sqrt[3]{8} \times \sqrt[3]{x^3} \times \sqrt[3]{y}$

$=2\sqrt[3]{2} \times 2\times x\times \sqrt[3]{y}$

= $2\times 2\times x\sqrt[3]{2y}$

$= 4x\sqrt[3]{2y}$

$4\sqrt[3]{54x^6y^5}=4\sqrt[3]{2\times 27 \times x^3\times x^3 \times y^3\times y^2} =4\sqrt[3]{2} \times \sqrt[3]{27} \times \sqrt[3]{x^3} \times \sqrt[3]{x^3} \times \sqrt[3]{y^3}\times\sqrt[3]{y^2}$

$=4\sqrt[3]{2} \times 3 \times x\times x \times y \times \sqrt[3]{y^2}$

$=12x^2y\sqrt[3]{2y^2}$

Therefore,

$3\sqrt[3]{16x^3y} + 4\sqrt[3]{54x^6y^5}$ =$4x\sqrt[3]{2y}$ +$12x^2y\sqrt[3]{2y^2}$