$\sqrt{2}$ is a rational number.

True

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False

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Solution

The correct option is B False
Square root of a prime number is always an irrational number as it cannot be represented in the form $\frac{p}{q}$ where $p, q$ are integers and $q$ is non-zero.

As $2$ is a prime number $\sqrt{2}$ is an irrational number.

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Question 25
Which of the following statements is always true?
(a) $\frac{x - y}{2}$ is a rational number between x and y.
(b) $\frac{x + y}{2}$ is a rational number between x and y.
(c) $\frac{x * y}{2}$ is a rational number between x and y.
(d) $\frac{x / y}{2}$ is a rational number between x and y.

Q. Is

(2 + \sqrt{3})

a rational number ?

Why √2/1 is not a rational number? Where p = √2 and q=1 which is satisfying the need for a rational number.

Q. Show that

2 + \sqrt{2}

is not a rational number.

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\frac{- 2}{3}

and

\frac{1}{2}

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√2 is a rational number.

The correct option is B FalseSquare root of a prime number is always an irrational number as it cannot be represented in the form pq where p,q are integers and q is non-zero.As 2 is a prime number √2 is an irrational number.

$\sqrt{2}$ is a rational number.

The correct option is B False
Square root of a prime number is always an irrational number as it cannot be represented in the form $\frac{p}{q}$ where $p, q$ are integers and $q$ is non-zero.

As $2$ is a prime number $\sqrt{2}$ is an irrational number.