8th Class Mathematics Squares and Square Roots Square Root Methods

         Square Root Methods

We know that addition is inverse of subtraction, multiplication is inverse of division, and similarly square root is the inverse of square of a number. There are different methods to find the square root of a number. We can find the square root either by finding the factors or by repeated subtraction or by long division method.  

            By Prime Factorization Methods

In this method we find the prime factors of the given number and then pair them up. We multiply the numbers taking one from each pair and get the square root of the required number. It is useful only in case the numbers have perfect pairs of prime factors.

\[\sqrt{256}=\sqrt{(2\times 2)\times (2\times 2)\times (2\times 2)\times (2\times 2)}\]

There are four such order pairs within the square root of the number, therefore, the square root of the above number is \[\text{2}\times \text{2}\times \text{2}\times \text{2}=\text{16}\]  

            Repeated Subtraction Method

In this method we subtract the successive odd numbers from the given number starting from 1 till we get the result zero. The number of steps required to reduce the given number to zero will be the square root of the given number.  

Take the number 64

Solution:

\[64-1=63\Rightarrow 63-3=60\Rightarrow 60-5=55\Rightarrow 55-7=48\]

\[\Rightarrow 48-9=39\Rightarrow 39-11=28\Rightarrow 28-13=15\Rightarrow 15-15=0\]

There are eight steps required to reduce the number to 0. Therefore, square root of 64 is 8.  

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