Question

Given that f >0 and g > 0, select all expressions that are equivalent to 5fg 15 19 A. 5f2 g 5.392 B. 5(19) – 15g C. 5fgì – 15g D. 59 (11 - 3) E. 59f2 32

Answer 1

We need to rewrite the expression to see the correct answers:

$\begin{gathered} We\text{ know that:} \\ \sqrt[]{f}=f^{\frac{1}{2}} \\ So, \\ 5\sqrt[]{fg}-15\sqrt[]{g}=5f^{\frac{1}{2}}g^{\frac{1}{2}}-5\cdot3g^{\frac{1}{2}},Option\text{ A is correct.} \\ 5\sqrt[]{fg}-15\sqrt[]{g}=5(fg)^{\frac{1}{2}}-15g^{\frac{1}{2}},\text{ Option B is correct and Option C is INCORRECT.} \\ 5\sqrt[]{fg}-15\sqrt[]{g}=5g^{\frac{1}{2}}(f^{\frac{1}{2}}-3),\text{ Option D is correct and Option E is I}NCORRECT. \end{gathered}$

Options A, B and D are CORRECT, Options C and E are INCORRECT.