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a is the product of 3 and the square root of 2, b is the
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09 Nov 2016, 15:30
09 Nov 2016, 15:30
Expert Reply
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Question Stats:
48% (03:44) correct
51% (04:19) wrong based on 31 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. \(64\)
A. \(1\)
B. \(30 - 12\sqrt{6}\)
C. \(36\)
D. \(30 + 12\sqrt{6}\)
E. \(64\)
Drill 3
Question: 11
Page: 292
Question: 11
Page: 292
Re: a is the product of 3 and the square root of 2, b is the
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09 Nov 2016, 15:37
09 Nov 2016, 15:37
Expert Reply
Explanation
Let’s translate this question, one step at a time.
a= \(3\sqrt{2}\), b = \(2\sqrt{3}\) and c= \(2\sqrt{6}\)
x = \((3\sqrt{2}+ 2\sqrt{3})^2\)
= \((3\sqrt{2}+ 2\sqrt{3})(3\sqrt{2}+ 2\sqrt{3})\)
= \(30+12\sqrt{6}\)
y = \(6(5 - 2\sqrt{6})\)=\(30-12\sqrt{6}\)
z = \(2^2*3^2\) =\(36\).
\(\frac{xy}{z}\)=\((30-12\sqrt{6})(30+12\sqrt{6})\frac{1}{36}\) = 1
Hence option A is correct.
Did you recognize the common quadratics? The product of x and y in the last chunk of the question contains one that could save you that intermediary step: \((x + y)(x - y) = x^2 - y^2\). Of course, it doesn’t take too much longer to write out the math.
Let’s translate this question, one step at a time.
a= \(3\sqrt{2}\), b = \(2\sqrt{3}\) and c= \(2\sqrt{6}\)
x = \((3\sqrt{2}+ 2\sqrt{3})^2\)
= \((3\sqrt{2}+ 2\sqrt{3})(3\sqrt{2}+ 2\sqrt{3})\)
= \(30+12\sqrt{6}\)
y = \(6(5 - 2\sqrt{6})\)=\(30-12\sqrt{6}\)
z = \(2^2*3^2\) =\(36\).
\(\frac{xy}{z}\)=\((30-12\sqrt{6})(30+12\sqrt{6})\frac{1}{36}\) = 1
Hence option A is correct.
Did you recognize the common quadratics? The product of x and y in the last chunk of the question contains one that could save you that intermediary step: \((x + y)(x - y) = x^2 - y^2\). Of course, it doesn’t take too much longer to write out the math.
Re: a is the product of 3 and the square root of 2, b is the
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23 Jun 2017, 13:36
23 Jun 2017, 13:36
You said x = 3 + 12*sqrt(6). This is not correct.
x = (3*sqrt(2)+2*sqrt(3))^2 = 30 + 12*sqrt(6).
x = (3*sqrt(2)+2*sqrt(3))^2 = 30 + 12*sqrt(6).
