Question

3. Which of the following are rational numbers?​

Answer 1

Answer:

a rational number is a number that can be expressed as the quotient or fraction qp of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.

Answer 2

Complete question:

Which of the following are rational numbers?​

(a)$(\sqrt{2})^2$ (b) $2\sqrt{2}$  (c) 2 + $\sqrt{2}$ (d) $\frac{\sqrt{2} }{2}$

Answer:

Option(a )$(\sqrt{2} )^{2}$ is a rational number.

Step-by-step explanation:

Explanation:

• Rational numbers include all whole numbers, integers, fractions, terminating decimals, and repeating decimals.

• Because they can only be expressed as decimals that never end and lack a recurring digit pattern, roots, radicals, and special numbers like pi are not rational numbers.

Now, we check whether  $(\sqrt{2})^2$ is rational or not.

First, we check whether $\sqrt{2}$ is rational or not.

⇒ $\sqrt{2}$ = 1.4142135

So, here we can see that $\sqrt{2}$ is a nonrepeating number.

Therefore, $\sqrt{2}$ is not a rational number.

Now, $(\sqrt{2})$ = 2, this can be written as $\frac{2}{1}$.

So, 2 is a rational number.

This means, $(\sqrt{2} )^2$ is a rational number but  $2\sqrt{2}$ , 2 + $\sqrt{2}$  and  $\frac{\sqrt{2} }{2}$ are not a rational number.

Final answer:

Hence, option(a )$(\sqrt{2} )^{2}$ is a rational number.

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