Which two choices are equivalent to this expression? 2sqrt (75)+3sqrt (50) A 2sqrt (25cdot 3)+3sqrt (25cdot 2) B 3sqrt (25)+2sqrt (25) C 10sqrt (3)+15sqrt (2) D 25sqrt (3)+25sqrt (2)

To determine which two choices are equivalent to the expression $2\sqrt{75} + 3\sqrt{50}$, we need to simplify the expression and compare it with the given choices.<br /><br />First, let's simplify the expression $2\sqrt{75} + 3\sqrt{50}$:<br /><br />$2\sqrt{75} + 3\sqrt{50} = 2\sqrt{25 \cdot 3} + 3\sqrt{25 \cdot 2}$<br />$= 2 \cdot 5\sqrt{3} + 3 \cdot 5\sqrt{2}$<br />$= 10\sqrt{3} + 15\sqrt{2}$<br /><br />Now, let's compare this with the given choices:<br /><br />A. $2\sqrt{25 \cdot 3} + 3\sqrt{25 \cdot 2}$<br />This choice is equivalent to the original expression, as it simplifies to $10\sqrt{3} + 15\sqrt{2}$.<br /><br />B. $3\sqrt{25} + 2\sqrt{25}$<br />This choice is not equivalent to the original expression, as it simplifies to $15 + 10$, which is not the same as $10\sqrt{3} + 15\sqrt{2}$.<br /><br />C. $10\sqrt{3} + 15\sqrt{2}$<br />This choice is equivalent to the original expression, as it is the same as the simplified form of the expression.<br /><br />D. $25\sqrt{3} + 25\sqrt{2}$<br />This choice is not equivalent to the original expression, as it simplifies to $25\sqrt{3} + 25\sqrt{2}$, which is not the same as $10\sqrt{3} + 15\sqrt{2}$.<br /><br />Therefore, the two choices that are equivalent to the expression $2\sqrt{75} + 3\sqrt{50}$ are A and C.