Question

What is the following sum? Assume x > 0 and y > 0 sqrt x^2y^2+2 sqrt x^3y^4+xy sqrt y

Answer 1

B is the right option

Explanation:

On edg :))

Answer 2

`xy(1+2y√(x)+√(y))`

Explanation:

Given expression,

`√(x^2y^2)+2√(x^3y^4)+xy√(y)`

`=(x^2y^2)^(1)/(2) + 2(x^3y^4)^(1)/(2) + xy√(y)`

`\because (√(x)=x^(1)/(2))`

`=(x^2)^(1)/(2) (y^2)^(1)/(2) + 2(x^3)^(1)/(2) (y^4)^(1)/(2) + xy√(y)`

`(\because (ab)^n=a^n b^n)`

`=x^{2* (1)/(2)} y^{2* (1)/(2)} + 2(x^{3* (1)/(2)})(y^{4* (1)/(2)})+xy√(y)`

`\because (a^n)^m=a^(mn)`

`=x^1 y^1 + 2x^{1(1)/(2)} y^2 + xy√(y)`

`=xy+2x.(x)^(1)/(2) y^2 + xy√(y)`

`=xy+2xy^2√(x)+xy√(y)`

`=xy(1+2y√(x)+√(y))`