The correct option is D irrational √(3) cannot be expressed in the form of p/q where p and q are integers and q≠0. Also, the value of √(3) is 1.732050..., whic ...

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Irrational Numbers

√3 is a/an - ...

Question

$\sqrt{3}$ is a/an ___ number.

natural

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whole

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rational

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irrational

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Solution

The correct option is D
irrational

$\sqrt{3}$ cannot be expressed in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$ . Also, the value of $\sqrt{3}$ is $1.732050...,$ which is a non-terminating and non-recurring decimal. Hence, it is an irrational number.

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Similar questions

\sqrt{3}

is a/an _______ number.

Q. Fill in the blanks to complete the proof of

1 + 7 \sqrt{3}

as an irrational number, provided

\sqrt{3}

is an irrational number.

Let’s assume

1 + 7 \sqrt{3}

be a rational number

\Rightarrow 1 + 7 \sqrt{3} = \frac{a}{b}, b \neq 0

\Rightarrow \sqrt{3} =

(i)___________ which is a (ii)_________ number.

\Rightarrow \sqrt{3}

is a rational number.
But

\sqrt{3}

is a/an irrational number.
Hence, we have arrived at a contradiction.

∵ 1 + 7 \sqrt{3}

is an irrational number.

Q. The number

(3 - \sqrt{3}) (3 + \sqrt{3})

is a/an .........

An unbiased die is thrown, what is the probability of getting
$(i)$ an even number of a multiple of $3$
$(i i)$ a number $3$ or $4$
$(i i i)$ a number greater than $3$

\sqrt{3}

is

(a) an integer
(b) a rational number
(c) an irrational number
(d) none of these

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√3 is a/an ___ number.

The correct option is D irrational √3 cannot be expressed in the form of pq where p and q are integers and q≠0. Also, the value of √3 is 1.732050..., which is a non-terminating and non-recurring decimal. Hence, it is an irrational number.

$\sqrt{3}$ is a/an ___ number.

The correct option is D
irrational

$\sqrt{3}$ cannot be expressed in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$ . Also, the value of $\sqrt{3}$ is $1.732050...,$ which is a non-terminating and non-recurring decimal. Hence, it is an irrational number.