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If (a=\sqrt{3}+\sqrt{2}) and (b=\sqrt{3}-\sqrt{2}), what is the value of (\frac{a-b}{a+b})?
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Answer and explanation
Correct answer: (\frac{\sqrt{6}}{3})
Step 1: (a-b=2\sqrt{2}) and (a+b=2\sqrt{3}). Step 2: (\frac{a-b}{a+b}=\frac{\sqrt{2}}{\sqrt{3}}=\frac{\sqrt{6}}{3}). Step 3: Do not forget to rationalize the denominator at the end.
Frequently asked questions
What is the correct answer to this question?
(\frac{\sqrt{6}}{3})
Why is this the correct answer?
Step 1: (a-b=2\sqrt{2}) and (a+b=2\sqrt{3}). Step 2: (\frac{a-b}{a+b}=\frac{\sqrt{2}}{\sqrt{3}}=\frac{\sqrt{6}}{3}). Step 3: Do not forget to rationalize the denominator at the end.
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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