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.
- 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
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
= 32×1/2 as we know that (am)n = am×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.
Key Things about 9
- 9 is a composite odd number.
- A square of length 3 unit has the area 9 unit2