Q18. - Algebra 2

Question

Name the sets of numbers to which each value belongs.

$-\sqrt{9}$

Step-by-Step Solution

Answer

$-\sqrt{9}$  belongs to the sets of integer, rational number, and real number.

Step 1 - Define different sets

• The set $\left\{1,2,3,4,5,...\right\}$ is called the set of natural number.
• The set $\left\{0,1,2,3,4,5,...\right\}$ is called the set of whole number.
• The set $\left\{-3,-2,-1,0,1,2,3,...\right\}$ is called the set of integer number.
• The set of rational number has numbers in the ratio form $\frac{m}{n}$, where $m$ and n are integers and n is non-zero. The decimal form of a rational number is either a terminating or repeating decimal.
• A real number that is not rational is irrational. The decimal form of an irrational number is neither terminating nor rational.
• Combine sets of rational and irrational number is real number.

Step 2 - Relationship between different sets

Following vein diagram shows relationship between different sets

Where, the symbols denote 

N- Natural number

W- Whole number

Z- Integers

Q- Rational number

I- Irrational number

R- Real numbers

Step 3 - Find the sets to which - 9 belongs

As, 9 is a integer number and square root of this number with minus sign is $-3$ which is also a integer number.

$-\sqrt{9}$ is a rational number and a real number.

 

Thus, $-\sqrt{9}$ belongs to the sets of integer, rational number, and real number.