Question

What is the following sum 5x(^3sqrt(x^2y)+2(^3sqrtx^5y)

Answer 1

[/tex]7x\sqrt[3]{x^2y}[/tex]

Step-by-step explanation:

The given equation is:

`5x\sqrt[3]{x^2y} +2√(3){x^5y}`

Solving this equation step by step

`5x\sqrt[3]{x^2y} +2√(3){x^5y}`

∵ x⁵ = x³ × x²

`5x\sqrt[3]{x^2y} +2\sqrt[3]{(x^3* x^2)y}`

take the x³ outside the cube root in second term

`5x\sqrt[3]{x^2y} +2x\sqrt[3]{(x^2)y}\\\sqrt[3]{x^2y} (5x+2x)\\7x\sqrt[3]{x^2y}`

Thus, last option is correct.

Answer 2

7x[∛x^2y]

Explanation:

given:

`5x\sqrt[3]{x^2y} +2\sqrt[3]{x^5y} \\5x(x^(2)/(3).y^(1)/(3)) + 2.x^(5)/(3).y^(1)/(3)    \\5x.x^(2)/(3).y^(1)/(3) + 2.x^(5)/(3).y^(1)/(3) \\5x^(5)/(3).y^(1)/(3) + 2.x^(5)/(3).y^(1)/(3) \\\\  y^(1)/(3) (5x^(5)/(3) + 2x^(5)/(3) )\\y^(1)/(3) (7x^(5)/(3)} )\\7\sqrt[3]{x^5y}\\ 7x\sqrt[3]{x^2y}` !