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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 x2 = 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. 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

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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 the Square Root of 9

What is the Value of the Square Root of 9?

The square root of 9 is 3.

Why is the Square Root of 9 a Rational Number?

Upon prime factorizing 9 i.e. 32, 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.

What is the Square of the Square Root of 9?

The square of the square root of 9 is the number 9 itself i.e. (√9)2 = (9)2/2 = 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.

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

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