Question

What is the following sum? Assume x≥0 and y≥0.

√x²y³ +2√x³y⁴+xy√y

A) x ²y² √y- 2xy²√x
B) 2xy √y + 2xy² √x
C) 4xy √x⁵y⁶
D) 2xy√xy

Answer 1

To simplify the given sum, we can simplify each term individually and then combine them.

Step-by-step explanation:

To simplify the given sum √x²y³ +2√x³y⁴+xy√y, we can first simplify each term individually.

• The first term, √x²y³, can be simplified as x^(2/2)y^(3/2) = xy^(3/2).
• The second term, 2√x³y⁴, can be simplified as 2x^(3/2)y^(4/2) = 2xy².
• The third term, xy√y, remains as it is.

Combining these simplified terms, we get xy^(3/2) + 2xy² + xy√y.

Therefore, the sum is xy^(3/2) + 2xy² + xy√y.