If (x=\sqrt{6}+\sqrt{2}) and (y=\sqrt{6}-\sqrt{2}), what is the simplified form of (\frac{x}{y})?
Answer and explanation
Correct answer: (2+\sqrt{3})
Step 1: Rationalize the denominator of (\frac{\sqrt{6}+\sqrt{2}}{\sqrt{6}-\sqrt{2}}). Step 2: The numerator becomes ((\sqrt{6}+\sqrt{2})^2=8+4\sqrt{3}), and the denominator is (6-2=4), so the value is (2+\sqrt{3}). Step 3: Multiplying by the conjugate is effective in such quotients.
Frequently asked questions
What is the correct answer to this question?
(2+\sqrt{3})
Why is this the correct answer?
Step 1: Rationalize the denominator of (\frac{\sqrt{6}+\sqrt{2}}{\sqrt{6}-\sqrt{2}}). Step 2: The numerator becomes ((\sqrt{6}+\sqrt{2})^2=8+4\sqrt{3}), and the denominator is (6-2=4), so the value is (2+\sqrt{3}). Step 3: Multiplying by the conjugate is effective in such quotients.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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