The square of an irrational number is always rational. Is the given statement true or false? Justify

Solution:

Consider an irrational number √3 and ∜3

Let us consider √3

By squaring it we get (√3)² = 3 which is the rational number

Let us consider (∜3)² = √3 which is irrational

Therefore, the statement is false.

✦ Try This: State whether the following statements are true or false? Justify your answer.

The square of √5 is always rational.

Consider an irrational number √5 and ∜5

Let us consider √5

By squaring it we get (√5)² = 5 which is rational number

Let us consider (∜5)² = √5 which is irrational

Therefore, the statement is false.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.2 Problem 3(v)

The square of an irrational number is always rational. Is the given statement true or false? Justify

Summary:

The statement “The square of an irrational number is always rational” is false

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