Given:
The radical expression is
[tex]7\sqrt[3]{8x^2y}+2\sqrt[3]{27x^5y^4}[/tex]
To find:
The value of the expression after addition.
Solution:
We have,
[tex]7\sqrt[3]{8x^2y}+2\sqrt[3]{27x^5y^4}[/tex]
It can be rewritten as
[tex]=7\sqrt[3]{2^3x^2y}+2\sqrt[3]{3^3x^3x^2y^3y}[/tex]
[tex]=7(2)\sqrt[3]{x^2y}+2\sqrt[3]{(3xy)^3x^2y}[/tex]
[tex]=14\sqrt[3]{x^2y}+2(3xy)\sqrt[3]{x^2y}[/tex]
[tex]=14\sqrt[3]{x^2y}+6xy\sqrt[3]{x^2y}[/tex]
Taking out the common factors, we get
[tex]=2\sqrt[3]{x^2y}(7+3xy)[/tex]
The value of given expression after addition is [tex]=2\sqrt[3]{x^2y}(7+3xy)[/tex].
