Question

Addition and Subtraction of Radical Expression

-Salamat

Answer 1

Given:

The radical expression is

`7\sqrt[3]{8x^2y}+2\sqrt[3]{27x^5y^4}`

To find:

The value of the expression after addition.

Solution:

We have,

`7\sqrt[3]{8x^2y}+2\sqrt[3]{27x^5y^4}`

It can be rewritten as

`=7\sqrt[3]{2^3x^2y}+2\sqrt[3]{3^3x^3x^2y^3y}`

`=7(2)\sqrt[3]{x^2y}+2\sqrt[3]{(3xy)^3x^2y}`

`=14\sqrt[3]{x^2y}+2(3xy)\sqrt[3]{x^2y}`

`=14\sqrt[3]{x^2y}+6xy\sqrt[3]{x^2y}`

Taking out the common factors, we get

`=2\sqrt[3]{x^2y}(7+3xy)`

The value of given expression after addition is
`=2\sqrt[3]{x^2y}(7+3xy)`.