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Which option is the rationalized form of (\frac{3}{2+\sqrt{5}})?
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Answer and explanation
Correct answer: (3(\sqrt{5}-2))
Step 1: The conjugate of the denominator is (2-\sqrt{5}). Step 2: (\frac{3}{2+\sqrt{5}}\times\frac{2-\sqrt{5}}{2-\sqrt{5}}=\frac{3(2-\sqrt{5})}{4-5}=3(\sqrt{5}-2)). Step 3: Use the difference of squares in the denominator when multiplying by a conjugate.
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What is the correct answer to this question?
(3(\sqrt{5}-2))
Why is this the correct answer?
Step 1: The conjugate of the denominator is (2-\sqrt{5}). Step 2: (\frac{3}{2+\sqrt{5}}\times\frac{2-\sqrt{5}}{2-\sqrt{5}}=\frac{3(2-\sqrt{5})}{4-5}=3(\sqrt{5}-2)). Step 3: Use the difference of squares in the denominator when multiplying by a conjugate.
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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