Square Root of Integers – Meaning, types and square root

What do you mean by the square root of integers 

An integer is a number that doesn’t have a decimal or fractional part. Integers range from negative to positive numbers, including zero.

Types of integers –

The following are the types on integers-

Positive Integers: An integer is said to be positive if it is greater than zero. Example: 1, 2, 3 and so on.

Negative Integers: An integer is said to be negative if it is less than zero. For example, -1, -2 and so on.

Is zero an integer?

Zero is neither a negative integer nor a positive one. Instead, it is a whole number.

Finding out square roots of positive integers –

Determining the square root of a positive integer is a piece of cake. There is little to no hassle in finding out these square roots. It is the same as taking a square root of any number.

However, square roots of integers either have a positive or a negative sign.

√16 can be written as 4 and as -4 as the minus sign gets turned into a positive sign after the number is squared.

Finding out square roots of negative integers –

Calculating the square root of a positive integer is relatively easier than that of a negative integer. It is, in fact, not practically possible to solve the square root of a negative integer.

This happens because a square root of a number is the value that gives the number when multiplied by itself. This is simply not possible in the case of negative numbers, as when two negative digits are multiplied, the result is always bound to be positive. When multiplied with itself, no number can ever yield a negative number, thereby making it complicated to solve the square root of a negative integer.

Finding out square roots of integers with an odd number of digits –

To calculate the square roots of a given integer with an odd number of digits, we follow these steps:-

Assumption – the given three digit integer is 289

Step 1:

Write 289 in pairs of digits.  Pair the digits beginning from the right. For example, 89 will be the first pair, and 2 will be left as a single digit.

Step 2:

We’ll find the integer part (i.e., the divisor) of the square root of the single digit on the left. In this case, the square root of 1 will give us 1. Here, we will consider 1 because its square root is less than 2. This will be the digit of the importance of the resultant square root. Write it at the top as the quotient. This is the current digit.

Step 3:

Now, we write the square of the current digit below the digit of significance and find the difference between the two (which is 1 here)—bringing down the next pair of digits on the right, i.e., 89, to append to the difference 1. The resultant number is then 189. We’ll call this the new number. This will complete our first stage of finding the digit of the significance of the square root.

Step 4:

On the left of the new number, we’ll write the double of the square root result formed till this stage. At this point, it will be just 2 (as 1×2=2). Next, we need to find a digit to append to 2 so that the product of the two-digit number formed and the digit appended is just less than or equal to the new number 189.

Appending 7 to 2 will form 27, and 7×27 gives us 189 with a remainder of 0. 7 now becomes the current digit, and it is appended to the square root result at the top to form 17 as the final square root.

This method stops when the remainder is 0.

Finding out the square root of integers with even number of digits –

To calculate the square roots of a given integer with an even number of digits, we follow these steps:-

Assumption – the given integer is 7921.

Step 1:

We begin by writing 7921 in pairs of digits from the right. The pairs thus formed are ’79’ ’21’.

Step 2:

Now the integer part (i.e., the divisor) of the square root of 79 is 8, and its square gives us 64. Here, we are considering 8 because its square root is less than 79. Subtracting 64 from 79 gives us 15 as a remainder. This number then becomes 15 21 when the next pair of digits is brought down. Thus, 8 is the current divisor and forms the digit of the significance of the square root result.

Step 3:

Square root result formed till now 8X2= 16. Now, by appending 9 to 16. We are considering 9 after a method of trials and errors. We get the new number as 169, so that 9×169=1521. 9 is appended to 8, and the square root result thus formed is 89. As the remainder becomes zero, the process ends, and 89 is our desired answer.