Square Root of 9

Square Root of 9 is equal to 3. It is represented as √9 or 9^1/2. The Square Root of a number is defined as the number that when multiplied by itself gives the original number. When multiplied by itself, √9 will result in the number 9. Hence, the value of the square root of 9 is 3.

In this article, we will learn what is the value of the square root of 9, how to find the value of the square root of 9.

The square root of 9 is denoted as √9. It is a rational number, meaning it results in a perfect square. When we talk about the square root of 9, we’re looking for a number that, when multiplied by itself, gives us number 9 i.e., 3 as 3 × 3 = 9.

Square Root of 9 is given as:

√9 = 3 × 3

Try out the following calculator to find out the square root of 9

Value of Square Root of 9

The numerical value of square root 9 is 3 which mean 9 is a perfect square.

√9 = √3² = 3

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The square root of a number is a value that, when you multiply it by itself, you get the original number. To find the square root, first, see if the number is a perfect square, which means its root is a whole number. It’s easier to figure out the square root of a perfect square than a number that’s not perfect.

For example, if we talk about first five natural numbers, then we are going to find their perfect square below:

As shown above {1, 4, 9, 16, 25},etc. are the perfect square.

Note: 9 is a Perfect Square.

To compute the square root of a non-negative number, we usually use these methods,

• Guess and Check Method
• Long Division Method
• Prime Factorization Method (Only for Perfect Square Number)

Let’s learn about these method in detail one by one .

In the Guess and Check method, we generally make a initial guess and then think it wisely and try to refine to get a number that is bit closer to the actual value.

Step 1: Begin by making an initial guess for the square root of the given number. As this depends on your understanding on perfect squares.

Step 2: Square your first guess, then multiply that number and check whether you find your number or not, If not then you need to move to next step , else you got your answer.

Step 3: If the result is too large, then you choose a large number you should think less than that number vice versa.

Step 4: You need to repeat the process until you get the original number.

Step 5: Once you got your special number for the original number, then you should check by multiplying by itself. Once you confirm, its sure that you had done a perfect approximation.

Now, Lets apply these steps for finding Square root of 9,

Step 1: Let’s start with the guess √9 = 3.

Step 2: Check whether when we multiply by itself it gives original number or not as 3 × 3 = 9, so you got the original number.

Step 3: So, you got square root of 9 by Guess and Check Method.

To find the square root of any number using Long Division, we can use the following steps:

Step 1: Group digits in pairs from the decimal point (if any) to the left and right.

Step 2: Find a number which is more suitable for the division or the number Whose Square is Less Than or Equal to the Original number.

Step 3: Subtract the perfect square from the first group of digits.

Step 4: Write down the next pair of digits.

Step 5: Double the current answer and find a digit to place next to it that, when multiplied by the new number, is less than or equal to the current number.

Step 6: Repeat steps 4-6 until desired accuracy is reached.

As We discussed earlier, 9 is a perfect square, So we get easily the square root by Long Division Method, Let’s discuss how we find it in the following steps:

Step 1: We must first write 9 as 9.000000 to make it easier to divide.

Step 2: Now, Check whether 9 is perfect square or not, and we find yes 9 is a perfect square.

Step 3: If we found the perfect square, then simply get your answer as the square root of the number.

Read More about Square Root by Long Division Method.

In this method, we normally perform the prime factorization and pair the factors to find the square root value. If we get a pair of every number, then we must say that number is a perfect square.

For a Perfect Square

Suppose, The number 16, if we talk about their Prime factors, We got {2, 2, 2, 2} as their prime factor. As we noticed every number has an Identical pair then, we must say 16 is a perfect square and then We need to multiply the one element of every pair to find the square root of the 16. Like, we got 2 pairs here {(2 , 2) , (2 , 2)} then we need to multiply one element of every pair. So [2×2=4], 4 is the Square root of 16.

For a Non-Perfect Square

If we find any number which is not a perfect square, then You need to perform similar process, We need to find their prime factors, then we must find a non pair number, like if we talk about 12, we got {2, 2, 3} as their prime factors. We get a non-pair element.

As we understand we may write any number X as √X × √X. So make a pair of any single number like this.

Prime factors pairs for 12 is {(2 × 2),(√3 × √3)}.

So Square root of 12 is (2 ×√3).

Prime Factorization of 9

As we know, 9 is a perfect square.

So, If we talk about their prime factors, We get {3 , 3}. As we write 9 as 3 × 3 so that we get 9.

√9 = 3

So, Square root of 9 is 3.

Learn More,

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What is the Value of Square Root of 9?

The value of the square root of 9, is 3.

Is Square Root of 9 Rational or Irrational Number?

Square Root of 9 i.e., √9 is an rational number as it can be written as √9 = 3.

Is 9 a Perfect Square?

Yes, 9 is a perfect square as it can be written as 3 × 3.

Is the Square Root of 9 Negative?

Square root of 9 is 3, which is an positive integer or a natural number.