Square Root of 9
The square root of 9 is expressed as √9 in the radical form and as (9)^{½} or (9)^{0.5} in the exponent form. The square root of 9 is 3. It is the positive solution of the equation x^{2} = 9. The number 9 is a perfect square.
 Square Root of 9: 3
 Square Root of 9 in exponential form: (9)^{½} or (9)^{0.5}
 Square Root of 9 in radical form: √9
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.
The square root of 9 is 3, because 3 multiplied by itself equals 9. Therefore, we can write the square root of 9 as √9 = 3. It is important to note that there are two possible solutions for the square root of any positive number, one positive and one negative. However, conventionally, when we write the square root of a number, we usually refer to only the positive solution. In the case of the square root of 9, the negative solution would be 3, because 3 multiplied by itself also equals 9.
Is the Square Root of 9 a Rational or an Irrational Number?
If a number can be expressed in the form p/q (where p and q are integers and q is nonzero), then it is a rational number. √9 = 3 can be written in the form of a fraction of integers as 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, 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
Square Root of 9 by Prime Factorization
The square root of a number can be found by prime factorization only when the number is a perfect square. If so, we group the pairs of prime factors, we collect only one number from each pair and multiply all resultant numbers which would give the square root of the number. To find the square root of 9 using prime factorization, we first prime factorize 9 by using its factor tree.
Thus, 9 = 3 × 3
It has only one pair of prime factors. As discussed earlier, we should take only one factor out of each pair to find the square root. Thus, √9 = 3.
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Important Notes on Square Root of 9:
 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 the 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.
Answer: 2/3

Example 2: 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
Answer: 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
Answer: 84
FAQs on the Square Root of 9
What is the Value of the Square Root of 9?
The square root of 9 is 3. Mathematically, square root of 9 can be 3 or 3. This is because both statements 3^{2} = 9 and (3)^{2} = 9 are true. But in general, the square root of 9 is considered to be 3 in many situations.
Why is the Square Root of 9 a Rational Number?
Upon prime factorizing 9 i.e. 3^{2}, we find that all the prime factors are in even power. This implies that the square root of 9 is a positive integer. Therefore, the square root of 9 is rational, as all integers are rational.
If the Square Root of 9 is 3. Find the Value of the Square Root of 0.09.
Let us represent √0.09 in p/q form i.e. √(9/100) = 3/10 = 0.3. Hence, the value of √0.09 = 0.3.
What is the Square of the Square Root of 9?
The square of square root of 9 is the number 9 itself i.e. (√9)^{2} = (9)^{2/2} = 9. This can be understood this way also: (√9)^{2} = 3^{2} = 9.
What is the Square Root of 9?
The square root of 9 is an imaginary number. It can be written as √9 = √1 × √9 = i √9 = 3i where i = √1 and it is called the imaginary unit.
What is the Value of 9 square root 9?
The square root of 9 is 3. Therefore, 9 √9 = 9 × 3 = 27.
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