# Square Root of 9 + Solution With Free Steps

9 is a perfect square and its square root is 3. Many people already know the square root of 9 but the article provides detailed steps. The long division method is used to prove that the square root of 9 is 3. The approximation method is also used for this purpose.

In this article, we will analyze and find the square root of 9 using various mathematical techniques, such as the approximation method and the long division method.

## What Is the Square Root Of 9?

The square root of the number 9 is 3.

The square root can be defined as the quantity that can be doubled to produce the square of that similar quantity. In simple words, it can be explained as:

√9 = √(3 x 3)

√9 = √(3)$^2$

√9 = ±3

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 3. Hence 3 is 9’s square root. The square root generates both positive and negative integers.

## How To Calculate the Square Root of 9?

You can calculate the square root of 9 using any of two vastly used techniques in mathematics; one is the Approximation technique, and the other is the Long Division method.

The symbol √ is interpreted as 9 raised to the power 1/2. So any number, when multiplied by itself, produces its square, and when the square root of any squared number is taken, it produces the actual number.

Let us discuss each of them to understand the concepts better.

### Square Root  of 9 by Long Division Method

The process of long division is one of the most common methods used to find the square roots of a given number. It is easy to comprehend and provides more reliable and accurate answers. The long division method reduces a multi-digit number to its equal parts.

Learning how to find the square root of a number is easy with the long division method. All you need are five primary operations- divide, multiply, subtract, bring down or raise, then repeat.

Following are the simple steps that must be followed to find the square root of 9 using the long division method:

### Step 1

First, write the given number 9 in the division symbol, as shown in figure 1.

### Step 2

Starting from the right side of the number, make a pair of the number 9 into pairs such as 09.

### Step 3

Now divide the digit 9 by a number, giving a number either 9 or less than 9. Therefore, in this case, the remainder is zero, whereas the quotient is 3.

### Step 4

This results in 9=9. The remainder obtained is 0. Move the next pair of zeros down and repeat the same process.

### Step 5

Keep on repeating the same steps till the zero remainder is obtained or if the division process continues infinitely, solve to two decimal places.

### Step 6

The resulting quotient y is the square root of 9. Figure 1 given below shows the long division process in detail:

### Important points

• The number 9 is a perfect square.
• The number 9 is a rational number.
• The number 9 can be split into its prime factorization.

## Is Square Root of 9 a Perfect Square?

The number 9 is a perfect square. A number is a perfect square if it splits into two equal parts or identical whole numbers. If a number is a perfect square, it is also rational.

A number expressed in p/q form is called a rational number. All the natural numbers are rational. A square root of a perfect square is a whole number; therefore, a perfect square is a rational number.

A number that is not a perfect square is irrational as it is a decimal number. As far as 9 is concerned, it is a perfect square. It can be proved as below:

Factorization of 9 results in 3 x 3 that can also be expressed as 3$^2$.

Taking the square root of the above expression gives:

= √(3$^2$)

= (3$^2$)$^{1/2}$

= 3

This shows that 9 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of 9 is equivalent to 3.

Images/mathematical drawings are created with GeoGebra.