If \(\sqrt{x}\) is irrational and (5) is rational, what type of number will \(5\sqrt{x}\) generally be when (5\ne0)?

Irrational number

Here, \(5\) is a non-zero rational number and \(\sqrt{x}\) is irrational. The product of a non-zero rational number and an irrational number is always irrational. Therefore, \(5\sqrt{x}\) is an irrational number. An integer and zero are both rational, so they cannot be the result here. Exam tip: Multiplication by zero is the exception that can make the product rational.

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.