Question

What is the following sum?

Answer 1

= 2(2x∛2y) +4(3x^2y∛2y^2)
= 4x (∛2y) + 12x^2y (∛2y^2)

Answer is A. first option

Answer 2

Option: A is the correct answer.

The sum is:

`4x(\sqrt[3]{2y})+12x^2y(\sqrt[3]{2y^2})`

Explanation:

We are given a expression as:

`2(\sqrt[3]{16x^3y})+4(\sqrt[3]{54x^6y^5})`

Since, the quantity which comes three times inside the cube root sign comes out as a single.

( i.e. if we have:

`\sqrt[3]{x^3}=x` )

Also,

`2(\sqrt[3]{16x^3y})=2(2x\sqrt[3]{2y})\\\\i.e.\\\\2(\sqrt[3]{16x^3y})=4x(\sqrt[3]{2y})`

( Since,

`16x^3y=2^3\cdot x^3\cdot 2y` )

Also,

`4(\sqrt[3]{54x^6y^5})=4(3x^2y\sqrt[3]{2y^2})\\\\i.e.\\\\4(\sqrt[3]{54x^6y^5})=12x^2y(\sqrt[3]{2y^2})`

( Since,

`54x^6y^5=3^3\cdot (x^2)^3\cdot y^3\cdot 2\cdot y^2` )

Hence, we get the simplified expression as:

`4x(\sqrt[3]{16x^3y})+12x^2y(\sqrt[3]{2y^2})=4x(\sqrt[3]{2y})+12x^2y(\sqrt[3]{2y^2})`