Question

simplify the following expression completely, where ( x geq 0 ).
( xsqrt{5xy^4} + sqrt{405x^3y^4} - sqrt{80x^3y^4} )
( \bigcirc quad xy^2sqrt{5x} + xy^2sqrt{405x} - xy^2sqrt{80x} )
( \bigcirc quad 6xy^2sqrt{5x} )
( \bigcirc quad -3xy^2sqrt{5x} + xy^2sqrt{405x} )
( \bigcirc quad 6xysqrt{5xy^2} )

Explanation:

Step1: Simplify each radical term

First term: $x\sqrt{5xy^4} = x \cdot y^2\sqrt{5x} = xy^2\sqrt{5x}$
Second term: $\sqrt{405x^3y^4} = \sqrt{81 \cdot 5 \cdot x^2 \cdot x \cdot y^4} = 9xy^2\sqrt{5x}$
Third term: $\sqrt{80x^3y^4} = \sqrt{16 \cdot 5 \cdot x^2 \cdot x \cdot y^4} = 4xy^2\sqrt{5x}$

Step2: Substitute back into expression

$xy^2\sqrt{5x} + 9xy^2\sqrt{5x} - 4xy^2\sqrt{5x}$

Step3: Combine like terms

$(1 + 9 - 4)xy^2\sqrt{5x} = 6xy^2\sqrt{5x}$

Answer:

B. $6xy^2\sqrt{5x}$