There is a number x such that x² is irrational but x⁴ is rational. Is the given statement true or false? Justify your answer by an example.

Solution:

Consider x = ∜2

Squaring on both sides

x² = (∜2)² = √2

Here √2 is an irrational number

x⁴ = (∜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 x² is irrational but x⁴ 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 x² is irrational but x⁴ is rational” is true

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