Maths-

General

Easy

Question

# Show the conjecture is false by finding a counterexample. The square root of any positive integer x is always less than x.

Hint:

### Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Counterexample: It is an example which shows that the conjecture is false.

## The correct answer is: Hence, the counterexample for the given conjecture is the number “0.01”.

### Let’s take the square root of 4, 9 and 16

We can see that the square root of the assumed positive number is less than the number.

But if we take 0.001. Its square root is

= 0.1

0.1 is greater than 0.01. So, the given conjecture is wrong as the square root of 0.01 is not less than 0.01

Final Answer:

Hence, the counterexample for the given conjecture is the number “0.01”.

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