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

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Math Expert
Joined: 02 Sep 2009
Posts: 59089
a is the product of 3 and the square root of 2, b is the product of 2  [#permalink]

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29 Jun 2018, 02:06
1
00:00

Difficulty:

65% (hard)

Question Stats:

64% (03:20) correct 36% (02:58) wrong based on 66 sessions

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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 $$\frac{xy}{z}$$?

A. $$1$$

B. $$30 - 12\sqrt{6}$$

C. $$36$$

D. $$30 + 12\sqrt{6}$$

E. $$64$$

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Math Expert
Joined: 02 Aug 2009
Posts: 8180
Re: a is the product of 3 and the square root of 2, b is the product of 2  [#permalink]

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29 Jun 2018, 03:05
a is the product of 3 and the square root of 2 = 3√2,
b is the product of 2 and the square root of 3 = 2√3 and
c is the product of 2 and the square root of 6=2√6
If x is the square of the sum of a and b = $$(3√2+2√3)^2=18+12+12√6=30+12√6$$
y is the product of 6 and the difference of 5 and c = 6*(5-2√6)=30-12√6
and z is the product of 2 squared and 3 squared, = $$2^2*3^2=36$$
what is $$\frac{xy}{z} = \frac{(30+12√6)(30-12√6)}{36}=\frac{30^2-12^2*6}{36}=(900-864)/36=36/36=1$$

A

A. $$1$$

B. $$30 - 12\sqrt{6}$$

C. $$36$$

D. $$30 + 12\sqrt{6}$$

E. $$64$$
_________________
Re: a is the product of 3 and the square root of 2, b is the product of 2   [#permalink] 29 Jun 2018, 03:05
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