Question

Which one of the following is not rational number
A)log5 with base10
B)5.32
C)143.12
D)10/18

Answer 1

Answer:

D)10/18

....................

Answer 2

The correct option is A.

Step-by-step explanation:

If a number is expressed in the form of p/q where, p and q are integers and q≠0, then it is called a rational number. Q is the set of rational numbers.

For example: 3,2.4, 4/9 etc.

$5.32=\dfrac{532}{100}=\dfrac{133}{25}\in Q$

$143.12=\dfrac{14312}{100}=\dfrac{3578}{25}\in Q$

$\dfrac{10}{18}\in Q$

Now we need to check whether $log_{10}5$ is rational or not.

Let $log_{10}5$ is a rational number.

$log_{10}5=\frac{p}{q}$

$5=10^{\frac{p}{q}}$         $[\because log_ab=x\Rightarrow b=a^x]$

$5^q=10^p$

$5^q=(2\cdot 5)^p$

$5^q=2^p\cdot 5^p$

It is not possible, because there is no 2 factors on the left side. So, out assumption is wrong and $log_{10}5$ is an irrational number.

Therefore, the correct option is A.

#Learn more

Which one of the following is a rational number ?????

,with proof​

https://brainly.in/question/14362427