Q65. - Algebra 2

Question

Name the sets of numbers to which each number belongs.

 

65. $\sqrt{7}$

Step-by-Step Solution

Answer

$\sqrt{7}$ belongs to Irrational (I) and Real (R).

Step 1 - Define real numbers.

A number that can be stated as an infinite decimal expansion. 

 

Real numbers are numbers that include both rational and irrational numbers.

Step 2 - State the explanation.

All numbers that is whole numbers, integers, natural number, rational and irrational numbers are real numbers.

 

Here, the number is $\sqrt{7}$. The value of $\sqrt{7}$ lies between 2 and 3.

 

As natural numbers are $\left\{1,2,3,...\right\}$. Then $\sqrt{7}$ is not a natural number.

 

As whole numbers are $\left\{0,1,2,3,...\right\}$. Then $\sqrt{7}$ is not a whole number.

 

And integers are $\left\{...,-3,-2,-1,0,1,2,3,...\right\}$. Then $\sqrt{7}$ is not an integer.

 

Since $\sqrt{7}$ cannot be expressed as $\frac{m}{n}$ form then it is not a rational number.

 

Then, it is an irrational number.

 

As it is an irrational number then it is a real number.

Step 3 - State the conclusion.

Therefore, the set of numbers to which $\sqrt{7}$ belongs is:

 

Irrational (I) and Real (R).