State whether the following statement is true or false. Justify your answers.

Every point on the number line is of the form \(\sqrt {m},\) where \(m\) is a natural number___

Every point on the number line is of the form \(\sqrt {m},\) where \(m\) is a natural number___

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State whether the following statement is true or false. Justify your answers.

Every point on the number line is of the form \(\sqrt {m},\) where \(m\) is a natural number___

Every point on the number line is of the form \(\sqrt {m},\) where \(m\) is a natural number___

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Since, on a number line, we can represent both negative as well as positive numbers.

Positive numbers are in the form of \(\sqrt{1}, \sqrt{1.1}, \sqrt{1.2} \ldots\) But, after taking square root of any natural number, we cannot get a negative number.

So, we don't get every point of number line.

Therefore, not every number on the number line is of form \(\sqrt{m},\) where \(m\) is a natural number.

Positive numbers are in the form of \(\sqrt{1}, \sqrt{1.1}, \sqrt{1.2} \ldots\) But, after taking square root of any natural number, we cannot get a negative number.

So, we don't get every point of number line.

Therefore, not every number on the number line is of form \(\sqrt{m},\) where \(m\) is a natural number.

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