Note that if a square has an area of 9 unit^{2}, then we use the value of the square root of 9 to find the length of the square. The value of the square root of 9 is 3. We denote the square root of 9 by the symbol √9. In this section, we will learn how to determine the value of √9.

Table of Contents

**Important Things:**

**9**is a perfect square.**√9 = 3****9**is the exponential form of square root of^{1/2}**9**.**√9**is the radical form of square root of**9**.- The square root of
**9**is**3.000**in decimal form. - Square of
**9: 9×9 = 81**

Let us now calculate the square root of 9.

**What is the Square Root of 9?**

The square root of 9 is 3. To prove this, we will write 9 as a square of some numbers. Observe that 9 is a product of two numbers of 3‘s. So we have

9=3×3=3^{2}

Taking square root on both sides, we get that

√9 = √3^{2}

As square root can be written as power 1/2, we have

√9 = (3^{2})^{1/2}

= 3^{2×}^{1/2} as we know that (a^{m})^{n }= a^{m×n}

= 3^{1 }= 3

So the value of the square root of 9 is 3.

**Is 9 a perfect square number?**

We have calculated above that √9=3. As 3 is a whole number so we get that the square root of 9 is a whole number. Thus by the definition of a perfect square, we conclude that 9 is a perfect square number.

**Square root of 9 by Prime Factorization**

To find the square root of 9 by the prime factorization method, we will factorize the number 9. We have

9 = 3×3 …(∗)

As 3 is a prime number, we cannot factorize further. So (∗) is the prime factorization of 9.

Taking square root on both sides of (∗), we get that

√9 = √3×3 = 3 as we know that √a×a=a

∴ the square root of 9 is 3.

**Is Square Root of 9 Rational?**

One knows that each rational number can be expressed as p/q with integers p and q (q ≠ 0).

From above we have √9=3.

Note that 3=3/1. So 3 can be expressed as p/q with p=3, q=1. This implies that 3 is a rational number. So the square root of 9 is also a rational number.

Conclusion: √9 is not an irrational number.

#### Key Things about 9

- 9 is a composite odd number.
- A square of length 3 unit has the area 9 unit
^{2}