how we find square root
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Step-by-step explanation:
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Answer:
To find the square root of any number, we need to figure out whether the given number is a perfect square or an imperfect square. If the number is a perfect square, such as 4, 9, 16, etc., then we can factorize the number by prime factorisation method. If the number is an imperfect square, such as 2, 3, 5, etc., then we have to use a long division method to find the root.
Hence, the methods to find the square root of numbers are:
Square Root by Prime Factorisation
Square Root by Repeated Subtraction Method
Square Root by Long Division Method
Square Root by Estimation Method
Let us learn each method of square root with examples.
Square root By Prime Factorisation
The square root of a perfect square number is easy to calculate using the prime factorisation method
24
Square Root by Repeated Subtraction Method
As per the repeated subtraction method, if a number is a perfect square, then we can determine its square root by:
Repeatedly subtracting consecutive odd numbers from it
Subtract till the difference is zero
Number of times we subtract is the required square root
For example, let us find the square root of 25.
25 – 1 = 24
24 – 3 = 21
21 – 5 = 16
16 – 7 = 9
9 – 9 = 0
Since, the subtraction is done for 5 times, hence the square root of 25 is 5.
Square Root by Long Division Method
Finding square roots for the imperfect numbers is a bit difficult but we can calculate using a long division method.
Square root by Estimation Method
This method is used as an approximation method, to find the square root by guessing the values.
For example, the square root of 4 is 2 and the square root of 9 is 3, thus we can guess, square root of 5 will lie between 2 and 3.
But, we need to check the value of √5 is nearer to 2 or 3. Let us find the square of 2.2 and 2.8.
2.22 = 4.84
2.82 = 7.84
Since the square of 2.2 gives an approximate value of 5, thus we can estimate the square root of 5 is equal to 2.2 approximately