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Class 10MathematicsReal NumbersIrrational numbersExpertLevel 13

If (x) is irrational and (x+\sqrt{2}) is rational, which can be a possible form of (x)?

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Answer and explanation

Correct answer: (3-\sqrt{2})

Step 1: To make (x+\sqrt{2}) rational, (x) should contain a (-\sqrt{2}) part. Step 2: If (x=3-\sqrt{2}), then (x+\sqrt{2}=3), which is rational. Step 3: Look for cancellation of the irrational part.

Tags

irrational cancellationexpressionclass 10

Frequently asked questions

What is the correct answer to this question?

(3-\sqrt{2})

Why is this the correct answer?

Step 1: To make (x+\sqrt{2}) rational, (x) should contain a (-\sqrt{2}) part. Step 2: If (x=3-\sqrt{2}), then (x+\sqrt{2}=3), which is rational. Step 3: Look for cancellation of the irrational part.

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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