Square Root of 9
Square root of 9 is usually expressed as √9. In this minilesson, you will learn about the square root of 9 which is equal to 3. We will look at a couple of interesting examples to know more about the square root of 9 and we will also calculate the square root of 9 using the long division method and by prime factorization. Now let's learn how to find the square root of 9 and let's check if the square root of 9 is a rational or irrational number.
 Square Root of 9: √9 = 3
 Square of 9: 9^{2 }= 81
1.  What Is the Square Root of 9? 
2.  Is Square Root of 9 Rational or Irrational? 
3.  How to Find the Square Root of 9? 
4.  FAQs on Square Root of 9 
What Is the Square Root of 9?
The square root of 9 is 3, i.e., multiplying 3 with 3 gives us 9. 3^{2 }= 3 × 3 = 9. Here 3 is called the square root of 9 and 9 is a perfect square.
Is the Square Root of 9 a Rational or an Irrational Number?
If a number can be expressed in the form p/q, then it is a rational number. √9 = ±3 can be written in the form of a fraction 3/1. It proves that √9 is a rational number.
How to Find the Square Root of 9?
Square roots can be calculated using various methods. Let us find the square root of 9 using prime factorization. We can express 9 as the product of its prime factor, which is, 3. 3 × 3 = 9 is a perfect square number.
Square Root of 9 by Long Division Method
To find the square root of 9 by the long division method, we need to follow the steps given below.
 Step 1: Make a pair of digits of the given number starting with a digit at the unit's place. Put a bar on each pair.
 Step 2: Now we have to multiply a number by itself such that the product is 9. Here, 3 × 3 = 9
Explore square roots using illustrations and interactive examples
Important Notes
 The square root of 9 is 3 and 3.
 9 is a perfect square number.
 The square root of a perfect square number can be easily found by prime factorization.
Square Root of 9 Solved Examples

Example 1 Solve square root of 4/9 using prime factorization.
Solution
Prime factorization of 4 = 2 × 2
Prime factorization of 9 = 3 × 3
Therefore, square root of 4/9 = √4 / √9 = √2 × √2 / √3 × √3 = 2/3. 
Example 2 Can you help Joe find the square root of 9/49?
Solution
Prime factorization of 49 = 7 × 7
Prime factorization of 9 = 3 × 3
Therefore, square root of 9/49 = √9 / √49 = √3 × √3 / √7 × √7 = 3/7 
Example 3 Find the sum of the square of 9 and the square root of 9.
Solution
Square of 9 = 81
Square root of 9 = 3
Therefore, sum of the square of 9 and the square root of 9 = 81 + 3 = 84
FAQs on Square root of 9
What is the square root of 9?
The square root of 9 is ±3.
How do you solve the square root of 9?
We can find the square root of 9 by prime factorization.
Since 3 × 3 = 9, we can express 9 as the product of the same number. Thus, 3 is the square root of 9.
How do you find a square root?
We can find the square root of a number by using different methods such as:
 Long division method
 Prime factorization
 Repeated subtraction method
What is the square root of a negative 9?
The square root of a negative number is not real. It is an imaginary number represented by i. For example, √−9 = 3i.
What is the value of √9 times √9?
The value of √9 × √9 = 9