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If (A=(3+\sqrt{2})^2-(3-\sqrt{2})^2), what is the correct value and nature of (A)?
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Answer and explanation
Correct answer: (12\sqrt{2}), irrational
Step 1: Use ((a+b)^2-(a-b)^2=4ab). Step 2: Here (a=3) and (b=\sqrt{2}), so (A=4\times3\times\sqrt{2}=12\sqrt{2}), which is irrational. Step 3: In such questions, use the identity instead of expanding both squares fully.
Frequently asked questions
What is the correct answer to this question?
(12\sqrt{2}), irrational
Why is this the correct answer?
Step 1: Use ((a+b)^2-(a-b)^2=4ab). Step 2: Here (a=3) and (b=\sqrt{2}), so (A=4\times3\times\sqrt{2}=12\sqrt{2}), which is irrational. Step 3: In such questions, use the identity instead of expanding both squares fully.
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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