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Square Root of 9

Square root of 9 is usually expressed as √9. In this mini-lesson, 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: 92 = 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. 32 = 3 × 3 = 9. Here 3 is called the square root of 9 and 9 is a perfect square.

square root of 9

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

square root of 9 by long division

Explore square roots using illustrations and interactive examples

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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

  1. 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. 

  2. 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

  3. 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

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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:

  1. Long division method
  2. Prime factorization
  3. 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

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