Square Root : The square root of  a given number is that number whose square is equal to the given number.

If   x² = y,  we say that square root of  ‘y’ is  ‘x’ and  we write, .

 e.g.  =  2,   =  25,    =  0.6  etc.

 ▪ If  the given number has  n  digits ( for integer  n ), the square root will contain  or   digits.

▪ A square root of  a negative number is a complex number. ( e.g.    =  2 i )

 ▪ A square root of  a number end with  2, 3, 7 or  8 never an integer.

■ Square root by Factorization : When a given number is a perfect square, we resolve, it into the product of  prime factors and take the product of  prime factors choosing one out of  every pair of  the same primes.

 e.g. Evaluate :

  2704  = 2²    2²  13²

= ( 2   2  13 )  =  52.

■ General  Method  :  First we extract the square root of  a given number and then we shall explain to make the ideas clear.

 e.g. Find the square root of   2524921.

 Solution.

■ Square root of  Decimal Fractions  :   We make even number of  decimal places by affixing a zero, if necessary. Now, we mark off periods and exact the square roots as shown in the following examples.

 e.g. (i) Evaluate  .

(ii) Evaluate  upto 2 decimal.

 Soln. 0.9 = 0.90 00 00  (Making even decimal places)

Important  Properties    :   (i)       (ii) 

(iii) 

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