Question

Give a counterexample for the statement all square roots are irrational numbers explain your reasoning

Answer 1

square root of 16 = 4....that is rational....so this is ur counter example.

The square root of a perfect square will produce a rational number. If u were to find the square root of a number that is not a perfect square, then that would produce an irrational number.

Answer 2

Statement: ALL square roots are irrational numbers.

Irrational is defined as a non-terminating real number.

✓4 = 2

2 is a terminating real number.

Therefore, 2 is rational.

The square root of 4 results in 2.

Therefore the square root of 4 results in a rational number.

Hence not all square roots result in irrational numbers.