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Class 10MathematicsReal NumbersIrrational numbersMediumLevel 15

If (\sqrt{k}) is irrational, which of the following results is necessarily rational?

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Answer and explanation

Correct answer: (\sqrt{k}\times\sqrt{k})

Step 1: Multiplying a square root by itself gives the number inside. Step 2: (\sqrt{k}\times\sqrt{k}=k), which is rational if (k) is an integer. Step 3: The square of an irrational square root can be rational.

Tags

real-numbersirrational-squarerational-result

Frequently asked questions

What is the correct answer to this question?

(\sqrt{k}\times\sqrt{k})

Why is this the correct answer?

Step 1: Multiplying a square root by itself gives the number inside. Step 2: (\sqrt{k}\times\sqrt{k}=k), which is rational if (k) is an integer. Step 3: The square of an irrational square root can be rational.

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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