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
• 9^1/2 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 = 3^2×1/2   as we know that (a^m)ⁿ = a^m×n

= 3¹ = 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.

• Basic concepts of square roots
• Properties of square roots

Key Things about 9

• 9 is a composite odd number.
• A square of length 3 unit has the area 9 unit²