Question

in the following numbers irritation number is
a) root16 - root 9
b) 3/4
c) 0.3333.........
d) 2+root3​

Answer 1

Answer:

(2+√3) is a irrational number.

So, option d is the correct answer.

Step-by-step explanation:

Here we have four options.

and we want to find irrational number among them.

We know,The numbers are all the real numbers that are not rational numbers is called irrational number.

For example,

$\frac{1}{2}$ is a rational number.So it is not a irrational number.

Again √2 is not a rational number.So we can say that √2 is a irrational number.

By option test,we can solve this question.

Option -1:

Here given $\sqrt{16} - \sqrt{9}$

Now,

$\sqrt{16} = 4 \\ \sqrt{9} = 3$

So,

$\sqrt{16} - \sqrt{9} \\ = 4 - 3 \\ = 1$

1 is a rational number.So it is not a irrational number.

Option -2:

Here number is $\frac{3}{4}$ which is a rational number.

So,It is not a irrational number.

Option -3:

Here given number is 0.33333........

Now,

$0.33333.... \\ = 0.3 \\ = \frac{3}{10}$

which is a rational number.

Therefore it is not a irrational number.

Option -4:

Given number is $2 + \sqrt{3}$

We know that √3 is a irrational number.

Therefore (2+√3) is a irrational number.

Know more about rational numbers,

https://brainly.in/question/16532538

https://brainly.in/question/38980520

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Answer 2

In the following numbers irrational number is d)$2+\sqrt{3}$

Definition of irrational number: Irrational numbers are real numbers that cannot be represented as simple fractions. An irrational number cannot be expressed as a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.

Here $\sqrt{3}$ cannot be expressed as a ratio and so $2+\sqrt{3}$ cannot be represented as simple fraction.

Other options:

a. $\sqrt{16} - \sqrt{9} =4-3=1$

here $1$ is not an irrational number

b. $\frac{3}{4}$ is already in a fraction format. Hence it is a rational number.

c. $0.3333......$ can be expressed as $3/10$. Hence it is also a rational number.

Hence the correct option is d) $2+\sqrt{3}$

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