​$${The HCF of } x^{1.5} \times y^{2.5} \text{ and } y^{3.5} \times x^{2.5} \text{ is }$$​

Correct option is A

Given:

Expressions: $$x^{1.5} \times y^{2.5}$$​ and $$y^{3.5} \times x^{2.5}$$​​

Formula used:

HCF of algebraic expressions = Product of the lowest powers of common variables

Solution:

For x:
Lowest power = min(1.5 , 2.5) = 1.5

For y:
Lowest power = min(2.5 , 3.5) = 2.5

Combining:

HCF =$$x^{1.5} \times y^{2.5}$$​

Write in terms of square root:

HCF=$$x \times y^2 \times \sqrt{(x \times y)}$$​