What is the following product? (2sqrt (7)+3sqrt (6))(5sqrt (2)+4sqrt (3)) 6sqrt (10)+16sqrt (2)+42 8sqrt (10)+30sqrt (2)+66 7sqrt (14)+6sqrt (21)+16sqrt (3)+21sqrt (2) 10sqrt (14)+8sqrt (21)+30sqrt (3)+36sqrt (2)

To find the product of $(2\sqrt {7}+3\sqrt {6})(5\sqrt {2}+4\sqrt {3})$, we can use the distributive property of multiplication over addition.<br /><br />Expanding the expression, we have:<br />$(2\sqrt {7}+3\sqrt {6})(5\sqrt {2}+4\sqrt {3}) = (2\sqrt {7})(5\sqrt {2}) + (2\sqrt {7})(4\sqrt {3}) + (3\sqrt {6})(5\sqrt {2}) + (3\sqrt {6})(4\sqrt {3})$<br /><br />Simplifying each term, we get:<br />$(2\sqrt {7})(5\sqrt {2}) = 10\sqrt {14}$<br />$(2\sqrt {7})(4\sqrt {3}) = 8\sqrt {21}$<br />$(3\sqrt {6})(5\sqrt {2}) = 30\sqrt {12} = 30\sqrt {4 \cdot 3} = 30 \cdot 2\sqrt {3} = 60\sqrt {3}$<br />$(3\sqrt {6})(4\sqrt {3}) = 12\sqrt {18} = 12\sqrt {9 \cdot 2} = 12 \cdot 3\sqrt {2} = 36\sqrt {2}$<br /><br />Adding up all the terms, we have:<br />$10\sqrt {14} + 8\sqrt {21} + 60\sqrt {3} + 36\sqrt {2}$<br /><br />Therefore, the correct answer is $10\sqrt {14}+8\sqrt {21}+30\sqrt {3}+36\sqrt {2}$.