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# 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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