a is the product of 3 and the square root of 2, b is the product of 2 and the

square root of 3, and c is the product of 2 and the square root of 6. If x is

the square of the sum of a and b, y is the product of 6 and the difference of

5 and c, and z is the product of 2 squared and 3 squared, what is XY/Z?

Ans:1

a = 3\sqrt{2}

b = 2\sqrt{3}

c = 2\sqrt{6}

x = {(3\sqrt{2}+ 2\sqrt{3})}^2 = {(3\sqrt{2})}^2+ 2(3\sqrt{2})(2\sqrt{3}) + {(2\sqrt{3})^2} = 9(2)+ 12\sqrt{2}\sqrt{3} + 4(3)

= 30 + 12\sqrt{6}

y = 6 (5 - 2\sqrt{6}) = 30 - 12\sqrt{6}

z = (2)^2(3)^2 = 36

\frac{xy}{z} = \frac{(30 + 12\sqrt{6})(30 - 12\sqrt{6})}{36} = \frac{(30)^2 - (12\sqrt{6})^2}{36}

= \frac{(30)(30) - (12)(12)(\sqrt{6}}{36} = \frac{(6)(5)(30) - (6)(12)(12)}{36}

= \frac{6\{150 - 144\}}{(6)(6)} = \frac{(6)(6)}{(6)(6)} = 1

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