Is sqrt-2- a rational number- - Maths Q-A

Define rational number :A number that can be expressed as p/q, where q 0 is known as a rational number.The value of √(2) is 1.414213..., that is non terminatin ...

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Standard IX

Mathematics

Irrational Numbers and Properties of Irrational Numbers

Is sqrt(2) a ...

Question

Is $\sqrt{2}$ a rational number?

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Solution

Define rational number :
A number that can be expressed as $\frac{p}{q}$ , where $q \neq 0$ is known as a rational number.
The value of $\sqrt{2}$ is $1.414213 . . .$ , that is non-terminating, exact value of $\sqrt{2}$ can not be determined.
we can not represent $\sqrt{2}$ as $\frac{p}{q}$ .
Hence, $\sqrt{2}$ is an irrational number.

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Is 2 a rational number?

Define rational number :A number that can be expressed as pq, where q≠0 is known as a rational number.The value of 2 is 1.414213..., that is non-terminating, exact value of 2 can not be determined.we can not represent 2 as pq.Hence, 2 is an irrational number.

Is $\sqrt{2}$ a rational number?