Square root of 9

The square of a number denotes the value when a number is multiplied by itself. Square root means to find the root number, which makes the given number a perfect square. It is denoted by the symbol √ known as radical or radix. For example, the square root of 10 is irrational, with never-ending digits after the decimal. On the other hand, the square root of 9 is rational. Therefore, a square root will always have a positive and a negative value.

Square root of 9 is ±3.

We need to check the unit place of a number to find the perfect square.

1. If the number ends with 2, 3, 7, and 8, then the number may not be a perfect square.

2. If the number ends with 1, 4, 5, 6, and 9, there is a possibility that the number may be a perfect square.

Square root of 9

9 is a perfect square. As said above, since the number ends with 9, therefore, there were chances that 9 would be a perfect square. 9 is a perfect square of 3. So if any number ends with 9, the chances are that the perfect square may end with 3. We can find the square root of 9 by the following two methods-

1. Using unit places

We know, number 9 is not a prime number. A prime number is the one that is divisible by 1 and the number itself. However, number 9 can be factored into 3 and 3. Hence, the number 9 is not a prime number.

We can write, 9 = 3 x 3.

Also, by putting the radical symbol on both sides, we get √9 = ±3.

√9 is exactly 3.

2. By long division method

1. Generally, in the long division method, we make pairs of the numbers after the decimal places. Since 9 is alone number, we do not need to make pairs.

2. Choose such a number that is a perfect square and is less than 9.

3. Write 3 at the place of divisor and quotient. We will get the remainder 0.

4. This is the long method to find the square root of 9. One can find square roots of 900, 9000, and so on with the same method.

5. This method is helpful to find the square root of any number. Even if they have decimal values, this method can also be used to find the square root.

Square root values to memorise

 √1 1 √11 3.3166 √2 1.4142 √12 3.4641 √3 1.7321 √13 3.6056 √4 2 √14 3.7417 √5 2.2361 √15 3.873 √6 2.4495 √16 4 √7 2.6458 √17 4.1231 √8 2.8284 √18 4.2426 √9 3 √19 4.3589 √10 3.1623 √20 4.4721

Do you know?

1. Ancient Indians have been using square roots since 800 BCE.

2. Mahavira, an ancient Indian mathematician, was the first one to announce the negative value of a square root.

3. The procedure to find out the square root of a number was written in the book Writings and Reckonings during the Han dynasty around 200 BCE.

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