Square Root of 9


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Square Root of 9

The square root of 9 is equal to 3. It is represented as √9 in radical form and 91/2 in exponential form. When we multiply a number by itself we get the square of the number. The square root of any number is a value that is multiplied by itself to get the original value. So, the square root of 9, denotes to reverse of the square of the number 9. If x is the square root of 9 then x2 = 9.

What is Square root of 9?

Square root of 9 is a whole number that is multiplied by itself to get the original number. The actual value of square root of 9 is 3.

√9 = ±3

If we square +3 or -3, the resulting value will be equal to 9.

  • (+3)2 = 9
  • (-3)2 = 9


Since, the square root of 9 results in a whole number, therefore, 9 is a perfect square.

Also, the root of 9 is a rational number, because we can represent √9 = ±3 in the form P/Q, such as 3/1.

How to Find Square Root of 9?

Number 9 is an odd number and not a prime number. Prime numbers have only two factors, 1 and the number itself. But as we know, 9 have three multiple factors, 1, 3 and 9 itself. Thus, we can write the number 9 in the form of multiple as;

1 × 9 = 9

3 × 3 = 9

9 × 1 = 9

You know that number 9 is a multiple of 3 or when 3 is multiplied by itself, we get the number 9. Therefore, we can write the square root of 9 as;

\(\sqrt{9}\) = \(\sqrt{3 × 3}\)

= \(\sqrt{3^2}\)

The square cancels the square root of a number. Therefore, if we cancel the square root with a square in the above expression, we get,

\(\sqrt{9}\) = ±3

Basically, the square root of a number gives two root values, one with +ve and another with -ve symbol. Therefore, the value of the square root of 9 can be expressed as +3 and -3 or we can say the roots of 9 are +3 and -3.

Number 9 is the perfect square as it fulfils the criteria which we discussed earlier in the introduction.

Square Root of 9 by Long Division Method

Long division method is helpful to find the square root of non-perfect squares. Since, 9 is a perfect square, thus, it is very easy to derive its square using division method. Remember the following points:

  • 9 is a single-digit number, thus its square root will be less than 9
  • 9 is an odd number, thus it is not divisible by any even number less than 9 (i.e.,2,4,6,8 is rejected)
  • We have to multiply the rest of the numbers 3, 5, and 7 with themselves to find the value equal to 9
  • Hence, 3 x 3 = 9
  • So, the square root of 9 is equal to 3

Important Points

  • If the number ends with 2, 3, 7 and 8, then the number is not a perfect square.
  • A perfect square number ends with 1, 4, 5, 6 and 9.
  • It is easy to find the square root of a perfect square number as it results in the whole number, whereas imperfect squares result in fractional or decimal numbers. We can easily square a number by just multiplying the number to itself but taking the square root of the number is a little complicated, especially in the case of imperfect squares.
  • The square root is represented by ‘√’ symbol. This symbol is named a radical symbol or radix. And the number underneath the radical symbol or radix is called the radicand. Here, we will find out the square root of 9 by a simple method, where 9 is the radicand.

Related Articles

Square Root of 9 Solved Examples

Q.1: What is the value of square root of 9/25?

Solution: Finding the root of 9 and 25 individually we have;

√9 = 3


√25 = 5

Thus, √(9/25) = 3/5

Q.2: Find the sum of √9 + 2√49.

Solution: Since,

√9 = 3

√49 = 7


√9 + 2√49 = 3 + 2 (7) = 3 + 14 = 17

Frequently Asked Questions – FAQs

What is actual value of square root of 9?

The value of square root of 9 is 3.

Is root 9 a rational or irrational?

Root 9 is a rational number because √9 = 3 can be expressed as 3/1.

What is the square root of -9?

The square root of -9 is 3i, since √-1 = i, where i is the imaginary number.

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