# There is a number x such that x^{2} is irrational but x^{4} is rational. Is the given statement true or false? Justify your answer by an example.

**Solution:**

Consider x = ∜2

Squaring on both sides

x^{2} = (∜2)^{2 }= √2

Here √2 is an irrational number

x^{4} = (∜2)^{4 }= 2

Here 2 is a __rational number__

Therefore, the statement is true.

**✦ Try This: **After rationalising the denominator of 5/(4√2 - 3√3), we get the denominator as

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

**NCERT Exemplar Class 9 Maths Exercise 1.2 Sample Problem 2**

## There is a number x such that x^{2} is irrational but x^{4} is rational. Is the given statement true or false? Justify your answer by an example

**Summary**:

The statement “There is a number x such that x^{2} is irrational but x^{4} is rational” is true

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