Answer

Verified

419.1k+ views

**Hint:**To find the relation between assertion and reason, we have to analyze each statement. We can see that the assertion states that 2 is a rational number. A rational number is a real number that can be represented in the form of $\dfrac{P}{Q}$ where P and Q are integers and $Q \ne 0$. From this, we can analyze whether the assertion is correct or not. Irrational numbers are real numbers that can be written in decimals but cannot be written as the ratio of two integers. They have endless non-repeating digits after the decimal point. We can write down the square roots of a few numbers like the first 10 real numbers to check whether the reason is true or not.

**Complete step-by-step solution**We need to find the relation between assertion and reason. In the assertion section, it is given that 2 is a rational number. Let us find what is a rational number.

A rational number is a real number that can be represented in the form of $\dfrac{P}{Q}$ where P and Q are integers and $Q \ne 0$. In other words, a rational number is a number that can be represented as the ratio of two integers.

Now, let us examine 2.

2 is a real number and can be written as \[\dfrac{2}{1}\], that is, the ratio of two integers. Hence 2 is a rational number.

We can see that the assertion statement is true.

Now, let us examine the reason statement.

It is given that the square roots of all positive integers are irrational.

Irrational numbers are real numbers that can be written in decimals but cannot be written as the ratio of two integers. They have endless non-repeating digits after the decimal point. For example, let us consider $\sqrt{2}=1.414....$ . We can see that they have long digits after the decimals.

Now, let us come back to the statement. Let us consider the square root of the first 10 positive integers as follows.

$\begin{align}

& \sqrt{1}=1 \\

& \sqrt{2}=1.414... \\

& \sqrt{3}=1.732... \\

& \sqrt{4}=2 \\

& \sqrt{5}=2.236... \\

& \sqrt{6}=2.449... \\

& \sqrt{7}=2.645... \\

& \sqrt{8}=2.828... \\

& \sqrt{9}=3 \\

& \sqrt{10}=3.162... \\

\end{align}$

We can see that all the square roots of positive integers are not irrational. For, example, let us observe 1, 4,9,16, etc. They form the square root of these perfect squares. They are rational numbers. We can also note that all perfect squares are rational numbers.

**Hence, we can say that the square roots of all positive integers are not irrational. Hence, the correct option is C.**

**Note:**Do not get confused with rational and irrational numbers. You may interchange the definitions of these like rational numbers that can be written in decimals but cannot be written as the ratio of two integers while irrational numbers can be expressed as a ratio of two integers. We can also observe that the numbers that form perfect squares are always rational.

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

In 1946 the Interim Government was formed under a Sardar class 11 sst CBSE

10 examples of law on inertia in our daily life

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE