# Square root of 9

Note that if a square has an area of 9 unit2, 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.

#### Important Things:

• 9 is a perfect square.
• √9 = 3
• 91/2 is the exponential form of square root of 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=32

Taking square root on both sides, we get that

√9 = √32

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

√9 = (32)1/2

= 31/2   as we know that (am)n = am×n

= 3= 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 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.