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Square Root of 9 is the value that gives the number 9 on multiplication with itself. The square root of 9 is 3. When 3 is multiplied by itself it gives the number 9, thus, it is the square root of 3. It is the reverse of the square of the number 9. The square root of 9 is represented as √9 in the radical form and (9)½ or (9)0.5 in its exponential form. It is also the positive solution of the equation x2 = 9.
The number 9 is a perfect square as the square root of 9, i.e. 3 is a whole number and can be represented in the p/q form. Every real number has two values of square root out of which one is positive and another is negative.
Read More: NCERT Solutions for Class 8 Mathematics Squares and Square Roots
Key Terms: Square Root of 9, Square Root, Multiplication, Whole Number, Prime Factorization, Long Division, Square
What is Square Root of 9?
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Square root of any natural number or a real number is the number that gives the value of the original number when multiplied by itself. The square root of 9 is 3. Since the square root of 9 is a whole number, thus, 9 is a perfect square.
The value of a square root has two values so the value of a square root of 9 will be ±3.
| √9 = ±3 |
If we square +3 or -3, the value obtained will be equal to 9.
- (+3)2 = 3 x 3 = 9
- (-3)2 = (-3) x (-3) = 9
![Square Root of 9]()
How to Find Square Root of 9?
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Square Root of a number can be obtained through various methods in mathematics which are as follows:
- Prime Factorization
- Long Division Method
- Average Method
- Repeated Subtraction Method
- Number Line Method
Square root of 9 can easily be found with the help of Prime Factorization and Long Division methods.
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Square Root of 9 by Prime Factorization
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Prime Factorization is one of the most common and easiest methods to calculate the square root. In this method, the number whose square root is to be found is denoted as a product of prime numbers. Similar prime numbers are grouped in pairs of two, and the product of one number from each pair is equal to the square root of the number.
The value of the square root of 9 is calculated by the prime factorization method as
√9 = √3 x 3 x 1 x 1
√9 = 3 x 1 = 3
Read More: Finding Square Roots through Prime Factorization
Square Root of 9 by Long Division Method
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Long division method is another method of calculating the square root of non-perfect squares. As 9 is a perfect square, its square root can easily be found using the long division method.
- 9 is a single digit number, so, its square root will always be less than 9.
- 9 is an odd number and hence is not divisible by any of the even numbers like 2, 4, 6, and 8.
Therefore, we need to multiply the rest of the numbers 3, 5, and 7 by themselves to find the value equal to 9. Thus,
3 x 3 = 9
Hence, the square root of 9 is 3.
Read More: Squares and Square Roots MCQs
Is Square Root of 9 Rational or Irrational?
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A number is said to be rational if it can be represented in the p/q form. We know that the square root of 9 is 3,
√9 = 3
Since 3 is a whole number, thus, it can be expressed in the p/q form as 3/1. Thus, the square root of 9 is a rational number.
Read More: Finding Square Root Through Repetitive Subtraction
Solved Examples on Square Root of 9
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Given below are a few solved examples on Square Root of 9:
| Example 1: Find the value of the square root of 9/25. Solution: First, we will find the square root of 9 and 25.
According to the question, √(9/25) Substituting the values, we get √(9/25) = 3/5 Example 2: What will be the sum of the square of 9 and the square root of 9? Solution: The square of 9 and the square root of 9 are
Adding them up, we get 81 + 3 = 84 Thus, the sum of the square of 9 and the square root of 9 is 84. |
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Things to Remember
- Square Root of 9 is the number that gives the value 9 when multiplied by itself.
- The square root of 9 is 3 and is represented as “√9”.
- The square root of 9 has two values which are +3 and -3.
- It can be calculated using the methods of prime factorization and long division.
- 9 is a perfect square number as its square is a whole number (3).
- The square root of 9, i.e. 3 is rational as it can be expressed in p/q form (3/1).
Sample Questions
Ques. What is Square Root? (2 Marks)
Ans. Square root of a number is a value, which gives the original number, on multiplication with itself. It is the inverse of the square of a number. For example, 5 is the square root of 25. It can be expressed as
- √25 = 5
- 5 x 5 = 25
Ques. What is the Square Root of 9? (2 Marks)
Ans. The square root of 9 is equal to 3. It is the value that gives the original number 9 on multiplication by itself.
√9 = 3
3 is the square root of 9 as
3 x 3 = 9
Ques. What is the Square Root of -9? (2 Marks)
Ans. Negative numbers don’t have real roots. It is an imaginary number. So, it can be written as √-9 = √-1 x √9 = i √9 = 3i, where the value of √-1 = I, which is an imaginary unit.
Ques. Find the square root of 9/49. (2 Marks)
Ans. The square root of 9 and 49 are
- Square Root of 9 = 3
- Square Root of 49 = 7
Thus, the square root of 9/49 = 3/7.
Ques. Is the square root of 9 Irrational? (1 Mark)
Ans. No, the square root of 9 is not an irrational number. It is a rational number because 3 can be written in the p/q form as 3/1. Thus, the square root of 9 is rational.
Ques. Calculate the square root of 9/16. (2 Marks)
Ans. We know that
- Square Root of 9 = 3
- Square Root of 16 = 4
Thus, Square Root of 9/16 = 3/4.
Ques. What is the square of the square root of 9? (2 Marks)
Ans. The square root of 9 is 3, and the square of 3 is 9.
√9 = 3
Squaring 3, we get
3 x 3 = 9
So, the square of the square root of 9 is 9, itself.
Ques. Find the square root of 4/9 using prime factorization. (2 Marks)
Ans. The square roots of 4 and 9 using prime factorization are
- Prime Factorization of 4 = 2 × 2
- Prime Factorization of 9 = 3 × 3
Square Root of 4/9 = √4 / √9 = √2 × √2 / √3 × √3 = 2/3
Thus, the square root of 4/9 using prime factorization is 2/3.
Ques. What are the different methods to calculate the square root of a number? (2 Marks)
Ans. The methods used to calculate the square root of a number are
- Prime Factorization Method
- Long Division Method
- Average Method
- Repeated Subtraction Method
- Number Line Method
Out of these methods, prime factorization and Long division methods are the most commonly used methods to find the square root of a number.
Ques. Calculate the square root of 9 by the average method. (2 Marks)
Ans. The number 9 lies between the square numbers 4 and 16 and whose square roots are 2 and 4 respectively. So, the average of the numbers 2 and 4 is:
(2+4)/2 = 6/2 = 3.
Thus, the square root o 9 by the average method is calculated as 3.
Ques. How is the square root of 9 written in exponential form? (1 Mark)
Ans. The square root of 9 is written as 9½ or 90.5 in exponential form.
Ques. Find the value of 9 square root 9. (2 Marks)
Ans. We know that the square root of 9 is 3. Thus, according to the question,
9 x Square Root of 9
9 x √9 = 9 × 3 = 27
Thus, the value of 9 square root 9 is 27.
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