Square Root of 9

When we multiply a number to itself we get the square of the number. So, the square root of 9, denotes to un-square the number 9.For example,

2 × 2 = 22 = 4

4 × 4 = 42 = 16

7 × 7 = 72 = 49

Therefore, in the above examples, 4,16 and 49 are the square numbers. Now to find out if a number is a perfect square or not, we need to check the unit place of the number.

  • If at the unit place, number ends with 2,3,7 and 8, then the number is not a perfect square.
  • If at the unit place, number ends with 1,4,5,6 and 9, then the number is a perfect square.

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 as radical symbol or radix. And the number underneath the radical symbol or radix is called as radicand. Here we will find out the square root of 9 by a simple method, where 9 is the radicand.

What is the square root of 9?

The square root of 9 is represented in the form of \(\sqrt{9}\). 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

From the above figures, you can see the 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, which is expressed as +ve and -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 squares as it fulfills the criteria which we discussed earlier in the introduction. In the same way, if we take the example of another perfect square number say 5, after getting squared, it gives the value as 52 = 5 × 5 = 25. Now taking the square root of 25, we get,

\(\sqrt{25}\) = \(\sqrt{5 × 5}\)

= \(\sqrt{5^2}\)

= ±5

Therefore, the roots of 25 are +5 and -5.

Similarly, you can try to find the square roots of other perfect squares such 81, 16, 64, etc.

Download BYJU’S – The Learning App and learn to find the squares and roots of numbers with the help of interactive videos.


Practise This Question

Which of the following shows 114 and 258 on a number line?