Question

Which one of the following is rational number

a) √49 b) √10 c) 1

√2

d) 4√5​

Answer 1

We have to find, which of the option is a rational number.

Solution:

Check the options:

a) $\sqrt{49}$

= 7, is a rational number.

b) $\sqrt{10}$

= 3.162..., is not a rational number.

c) 1$\sqrt{2}$

= 1.14421..., is not a rational number.

d) 4$\sqrt{5}$

= 4 × 2.2360..., is not a rational number.

Thus, the required option is "a) $\sqrt{49}$".

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which one of the following is rational number

a) √49

b) √10

$\displaystyle \sf{c) \: \: \frac{1}{ \sqrt{2} } }$

d) 4√5

CONCEPT TO BE IMPLEMENTED

RATIONAL NUMBER

A Rational number is defined as a number of the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

IRRATIONAL NUMBER

A number which is not rational number is called irrational number

EXAMPLE

1. $\displaystyle \sf{2,- 1, \frac{1}{3} , - \frac{12}{23}} \: are \: the \: examples \: of \: rational \: numbers$

$\displaystyle \sf{2. \: \sqrt{3} \: , \: \frac{1}{ \sqrt{2} } } \: \: are \: \: irrational \: \: number$

EVALUATION

CHECKING FOR OPTION (a)

$\sf{ \sqrt{49} = 7 }$

Since √49 can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

So √49 is a rational number

Hence this option is CORRECT

CHECKING FOR OPTION (b)

Here the number is √10

Since √10 can not be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

So √10 is not rational number

Hence this option is NOT CORRECT

CHECKING FOR OPTION (c)

Here the given number is

$\displaystyle \sf{ \: \: \frac{1}{ \sqrt{2} } }$

Since this number can not be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

So

$\displaystyle \sf{ \: \: \frac{1}{ \sqrt{2} } }$ is not rational number

Hence this option is NOT CORRECT

CHECKING FOR OPTION (d)

Here the given number is 4√5

Since 4√5 can not be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

So 4√5 is not rational number

Hence this option is NOT CORRECT

FINAL ANSWER

The correct option is a) √49

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