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# Does a square root have two values?

• Last Updated : 03 Sep, 2021

The number system is defined as the system to represent different numbers. It is a mathematical representation of the given set of numbers by using digits or different numbers in a fixed manner. It helps to represent every number uniquely and shows the arithmetic structure of the figures. It also helps to operate mathematical operations such as addition, subtraction multiplication, and division. In mathematics, there are multiple types of number systems such as binary, decimal, octal, etc.

A number is defined as a mathematical value that is used for counting, measuring or labeling objects. Numbers are used to performing mathematical calculations. There are different types of numbers, natural numbers, whole numbers, rational numbers, irrational numbers, etc.

### Types of numbers

• Natural numbers are the counting numbers that have a set of positive integers from 1 to infinity. Natural numbers are represented by N. For eg- 1, 2, 3, 4, …
• Whole numbers are the set of numbers with all natural numbers and zero. They are represented by W. For eg- 0, 1, 2, 3, …
• Integers are the set of whole numbers with a negative set of natural numbers. They are represented by Z. For eg- …, -2, -1, 0, 1, 2, …
• Real numbers are any number positive integers, negative integers, decimal numbers, fractions without imaginary numbers are known as real numbers. They are represented by R. For eg- 0.67, 12/5, 0, -32, 10, etc
• Rational numbers are written as the ratio of one number over another number (p/q). They are represented by Q. For eg- 9/4, 6/5, 1/9, etc.
• Irrational numbers are numbers that cannot be expressed in the form of p/q. They are represented by P. For eg- √2, pi, etc.

### What is a Square?

The square of a number is defined as the value obtained by the multiplication of the number by itself. The exponential form of a square of a number x is written as x2. For eg- The square of 2 is 22 = 2 × 2 = 4.

The square of a negative number is also a positive number. For eg- The square of -2 is (-2)2 = -2 × -2 = 4. From the above two examples, it can be seen that the square of positive and negative numbers is always positive.

What is a Square Root?

The square root of a number is the inverse operation of the square. If the square root of a number x is y, then the square of y is x. The exponential form of the square root is written as x-2. The square root of the number x is represented as √x. For eg- The square root of 25 is √25=√(52)=5.

### Does a square root have two values?

Solution:

The square root of a number always has two answers, one is positive and one is negative. There are two answers because the square of a negative and positive number is the same. For eg- The square of 3 is 9 and the square of -3 is also 9. So the square root of 9 is 3 and -3. Similarly, the square root of a number y is x and -x.

### Similar Questions

Question 1: Calculate the square root of 36?

Solution:

Given that the number is 36.

Write the number as the multiplication of its prime factors.

36 = 2 × 2 × 3 × 3

36 = 22 × 33

Now calculate the square root of the numbers.

√36 = √(22 × 32)

√36 = 2 × 3

√36 = ±6

Hence, the square root of the given number is 6 and -6.

Question 2: Calculate the square root of 144?

Solution:

Given that the number is 144.

Write the number as the multiplication of its prime factors.

144 = 2 × 2 × 2 × 2 × 3 × 3

144 = 24 × 32

Now calculate the square root of the numbers.

√144 = √(24 × 32)

√144 = 4 × 3

√144 = ±12

Hence, the square root of the given number is 12 and -12

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