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16 Sep 2014, 01:24
Kudos
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Which of the following is equal to \(\frac{1}{2 - \sqrt{3}}\)?
A. \(\sqrt{3} - 2\)
B. \(2 + \sqrt{3}\)
C. \(\sqrt{2} + \sqrt{3}\)
D. \(2 - \sqrt{3}\)
E. \(\sqrt{3} + 4\)
A. \(\sqrt{3} - 2\)
B. \(2 + \sqrt{3}\)
C. \(\sqrt{2} + \sqrt{3}\)
D. \(2 - \sqrt{3}\)
E. \(\sqrt{3} + 4\)
16 Sep 2014, 01:24
Kudos
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Official Solution:
Which of the following is equal to \(\frac{1}{2 - \sqrt{3}}\)?
A. \(\sqrt{3} - 2\)
B. \(2 + \sqrt{3}\)
C. \(\sqrt{2} + \sqrt{3}\)
D. \(2 - \sqrt{3}\)
E. \(\sqrt{3} + 4\)
Rationalize the fraction by multiplying both the numerator and the denominator by \((2 + \sqrt{3})\). The purpose of rationalization is to eliminate irrational expressions in the denominator and simplify the expression:
\(\frac{2 + \sqrt{3}}{(2 + \sqrt{3})(2 - \sqrt{3})} = \)
\(=\frac{2 + \sqrt{3}}{4 - 3} = \)
\(=2 + \sqrt{3}\).
Answer: B
Which of the following is equal to \(\frac{1}{2 - \sqrt{3}}\)?
A. \(\sqrt{3} - 2\)
B. \(2 + \sqrt{3}\)
C. \(\sqrt{2} + \sqrt{3}\)
D. \(2 - \sqrt{3}\)
E. \(\sqrt{3} + 4\)
Rationalize the fraction by multiplying both the numerator and the denominator by \((2 + \sqrt{3})\). The purpose of rationalization is to eliminate irrational expressions in the denominator and simplify the expression:
\(\frac{2 + \sqrt{3}}{(2 + \sqrt{3})(2 - \sqrt{3})} = \)
\(=\frac{2 + \sqrt{3}}{4 - 3} = \)
\(=2 + \sqrt{3}\).
Answer: B
12 Oct 2014, 09:52
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Bunuel
Bunuel,
I'm just curious about what the intuition is behind this type of solution. How do we know we should multiply by \((2 + \sqrt{3})\) as opposed to some other expression, or rather than just solving every answer in raw form?
