Question

which of the following numbers is irrational ? a) √36 b) 0.85 c) 31.480152 d) 1.4343434​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

which of the following numbers is irrational

a) √36

b) 0.85

c) 31.480152...

d) 1.4343434

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 ≠ 0

EVALUATION

CHECKING FOR OPTION : (a)

Here the given number is √36

√36 = 6

So the number can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So the number is rational

CHECKING FOR OPTION : (b)

Here the given number is 0.85

$\displaystyle \sf{ = \frac{85}{100} \: }$

$\displaystyle \sf{ = \frac{17}{20} \: }$

So the number can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So the number is rational

CHECKING FOR OPTION : (c)

Here the given number is 31.480152..

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

Where p & q are integers with q ≠ 0

So the number is irrational

CHECKING FOR OPTION : (d)

1.4343434

$\sf{ = 1. \overline{43}}$

$\displaystyle \sf{ = \frac{142}{99} \: }$

So the number can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So the number is rational

FINAL ANSWER

Hence the correct option is c) 31.480152...

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Answer 2

Given :- which of the following numbers is irrational ?

a)√36 b) 0.85 c) 31.480152___ d) 1.4343434___

Solution :-

we know that,

• An irrational number is the number which can not be written in the form of p/q or say fraction. (where q ≠ 0.)
• The decimal expansion of an irrational number is non terminating non recurring . { Number does not repeat. }

so, checking given options we get,

a) √36

→ √36 = 6 = (6/1) = (p/q)

as we can see that, √36 can be written in the form of p/q and q is not equal to zero . Therefore, √36 is a rational number .

b) 0.85

→ 0.85 = 85/100 = 17/20 = (p/q)

as we can see that, 0.85 can be written in the form of p/q and q is not equal to zero . Therefore, 0.85 is a rational number .

c) 31.480152____

as we can see that, numbers in given decimal are not repeating . we can conclude that, the decimal expansion is non terminating non recurring .

Therefore, 31.480152____ is an irrational number .

d) 1.4343434___

Let,

→ m = 1.434343___ ------- Eqn.(1)

→ 100m = 143.4343___ ------ Eqn.(2)

subtracting Eqn.(1) from Eqn.(2) ,

→ 99m = 142

→ m = 142/99 = p/q

as we can see that, 1.4343434___ can be written in the form of p/q and q is not equal to zero . Therefore, 1.4343434___ is a rational number .

Hence, option (c) is correct answer .

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