Solution: The square root of 9 is 3
Methods
What is the Square Root of 9?
To start with, let’s review what we define as the square root of a number. A square root of a number is a number that when multiplied by itself gives the original value. So, for instance, the square root of 16 is 4 or √16 = 4, then by definition, we can also say that 4 • 4 is also 16. Now, for the Square Root of 9, the value is 3. It is noteworthy that the result of a square root can be either a whole number or a decimal.
Is the Square Root of 9 rational?
Oftentimes when it comes to square roots, it is helpful to know if the value of the square root is rational or irrational. A rational number is when you have a number that can be written as a fraction that divides two integers (as long as the denominator is not 0). Whole numbers can also be rational numbers! So, an irrational number would be a decimal that cannot be written as a fraction and is considered to go on and on with no end (non-terminating). In this case, because the square root of 9, 3, is a whole number (and not a decimal), we say that 9 is rational.
How do you find the Square Root of 9?
There are two main ways to calculate the Square Root of a number: perfect squares and long division. Generally speaking, the first method that uses perfect squares is one of the easier and efficient methods when the number you have is a perfect square. To reiterate, a perfect square occurs when the value of the square root is a whole value. On the other hand, long division is used when the value of the square root is a decimal or not a perfect square.
Our first attempt will be to try to see if we can use perfect squares. So, let's see if we can rewrite 9 as a product of a number times itself. Well, we know the common perfect square of:
3
×
3
=
9
3 × 3 = 9
3 × 3 = 9
Therefore:
9
=
3
2
=
3
\sqrt{9} = \sqrt{ 3^{2} } = 3
9 = 3 2 = 3
Thus, helping us arrive at the conclusion that the Square Root of 9 is 3.
Find The Square Root of Other Numbers
Finding the square root of any number can be done using the same method as shown above. Take a look how to find the square root of these other specific examples, by clicking on the any of the links below:
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