Those numbers which are obtained by squaring an integer or a whole number are known as perfect squares. A perfect square can also be defined as the number that is represented or expressed as the exponent (second) of the integer given. For instance, the number 25 is a perfect square as the square of 5 gives the value 25. Similarly, 21 is not a perfect square because it cannot be expressed or represented as the second exponent of the integer. The formula for a perfect square number is N = x.x where ‘n’ is the product of the x. Let us take an example where x = 9. Here the perfect square will be equivalent to 81 as n = x.x, n = 9.9 = 81. Therefore, 81 is a perfect square number.
Tips and Tricks to Identify a Perfect Square
As mentioned above, the numbers which are obtained by squaring an integer or a whole number are known as perfect squares. The points mentioned below analyze the tips and tricks to identify a perfect square.
- The number ending with 7 and 3 respectively may have 9 as the unit place digit for the square number.
- Those numbers which end with 5 will have 5 as the unit place digit for the square number.
- Likewise, a number ending with 4 and 6 will have the unit place digit number as 6 for the square number.
Square Root
The factor of a number that gives an original number when multiplied by itself can be defined as the square root. It can also be considered as the inverse operation of squaring a given number. The square root of a number and the square are different. The above line signifies the square of a number. The square root of a number is the factor of that number which when multiplied by itself gives the original numbers. For example l, the square of 2 is 4. This can be explained as, if a is the square root of the b then, the product of a is b or a * a = b. The square of any number is always positive. For instance, the square root of both positive and negative 2 is 4 i.e. -2 * -2 = 4 or 2 * 2 = 4. The square root is denoted by a symbol known as radical and the number beneath it is known as the radicand. For example, ‘√ ‘ is radical, and the number ‘√ 4’ beneath it is known as the radicand.
How to Find a Square Root of Any Number?
To recall, the factor of a number that gives an original number when multiplied by itself can be defined as the square root. The following points mentioned below analyze the different processes of finding a square root of any number. They are:
- The process by which we subtract the consecutive odd number by the number whose square root is being found until we reach the number 0 is known as the process of repeated subtraction of the square root.
- The prime factorization method: The following are the steps of finding a square root with the help of prime factorization.
- Step 1: The first step is to divide the given number into as many as factors possible.
- Step 2: The second step is to form the pairs of those factors. For example, the pair of 2 or 4 and so on.
- Step 3: Now, you can take anyone factor from the pair. Then, you may find the product of that factor which is obtained by taking one factor of the pairs made.
- Step 4: The product that you got is the square root of the given number. If you follow the steps mentioned above in the correct manner, you nay get the square root of any number.
3. The third process is the square root by the estimation method. It refers to the reasonable guess of a given value to make the equation more realistic and easier. This method involves estimating a square root of a given number.
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