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If (a=\sqrt{2}+\sqrt{3}) and (b=\sqrt{3}-\sqrt{2}), what is the value of (ab)?
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Answer and explanation
Correct answer: (1)
Step 1: View (ab) as ((\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})). Step 2: This equals ((\sqrt{3})^2-(\sqrt{2})^2=3-2=1). Step 3: Since addition order does not change the sum, recognize the conjugate form.
Frequently asked questions
What is the correct answer to this question?
(1)
Why is this the correct answer?
Step 1: View (ab) as ((\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})). Step 2: This equals ((\sqrt{3})^2-(\sqrt{2})^2=3-2=1). Step 3: Since addition order does not change the sum, recognize the conjugate form.
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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