square-root-symbolThe square root of a number is that number, the square of which is equal to the given number. There are two types of square root of a number Positive and Negative. Symbol showed above is the pictorial representation for "Square Root" also Square Root is represented by (number)(1/2).

 Example: 49 has two roots 7 and -7, because (7)2 = 49 and (-7)2 = 49. Hence, we can write  (49)1/2 = ±7. 

Tricks (formula) for solving never ending square roots:   

tricky-infinite-square-root-formula (i)  If the problem figure is of the type Fig.1 then, directly answer can be written as x (given number).

infinite-square-root-formula
 
 (ii) If the problem figure is of the type Fig.2 then, find the factors of x, such that thedifference between the factors is 1, then the larger factor will be result.

tricky-infinite-square-root-formula

 

 


Some solved examples for infinite roots:

Never-Ending-Infinite-Square-Root-solved-example

 1) This example can be solved with the help of previously sited Square Root Formula(ii). Since 56 is the multiple of two consecutive numbers 7 and 8 and since 8>7. So, applying this Square root formula solution for above problem is 8.

Never-Ending-Infinite-Square-Root-solved-example 2) This example can be solved with the help of previously sited Square root Formula (i). Suppose the given expression is taken as "x" then x2 = 7x  i.e., x = 7, thus directly we can apply the above identity to solve problems like of above.

Never-Ending-Infinite-Square-Root-solved-examples3) This is same as of the previous example. Only difference is in representation of numbers. If you look at the series 625, 252 = 625, 54 = 625.....all the numbers were same, only trick is applied on indexing the factors of 625. Thus directly solution for the above square root problem can be written as 625.

Never-Ending-Infinite-Square-Root-solved-example
Never-Ending-Infinite-Square-Root-solved-example 
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