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Subjects
Class 10MathematicsReal NumbersIrrational numbersMediumLevel 15

If (\sqrt{p}) is irrational and (k) is a non-zero rational number, what type of number is (\frac{\sqrt{p}}{k})?

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Answer and explanation

Correct answer: Irrational

Step 1: Dividing by a non-zero rational number does not remove irrationality. Step 2: For example, (\frac{\sqrt{3}}{4}) remains irrational. Step 3: The condition (k\neq0) is necessary because division by zero is not possible.

Tags

real-numbersirrational-ruledivision

Frequently asked questions

What is the correct answer to this question?

Irrational

Why is this the correct answer?

Step 1: Dividing by a non-zero rational number does not remove irrationality. Step 2: For example, (\frac{\sqrt{3}}{4}) remains irrational. Step 3: The condition (k\neq0) is necessary because division by zero is not possible.

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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