Question

I NEED HELP!!!!!

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

a- 7x(^6 square root of x^2y)
b-7x^2(^6 square root of xy^2)
c-7x^2(^3 square root of xy^2)
d-7x(^3square root of x^2y)

Answer 1

d-7x(^3square root of x^2y)

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

For this case we have the following function:

`5x\sqrt[3]{x^2y} + 2 \sqrt[3]{x^5y}`
Rewriting we have:

`5x\sqrt[3]{x^2y} + 2 \sqrt[3]{x^3x^2y}`
Then, by properties of exponents we have:

`5x\sqrt[3]{x^2y} + 2x\sqrt[3]{x^2y}`
Then, adding both quantities we have:

`7x\sqrt[3]{x^2y}`
Answer:
the following sum is:
d-7x(^3square root of x^2y)